Medium is where most scores are actually won and lost. These questions are not tricky for the sake of it, but every one of them has a wrong answer built to catch a specific shortcut.
Every question below is a real item from the SAT Climb bank, tagged medium by the same difficulty model the app uses to build your practice. Pick an answer before you open the explanation.
Math · Geometry and Trigonometry~2 per testMedium tier
In the xy-plane, line m is parallel to line n. Line p intersects line m at point A, forming an angle that measures 65°. Line p intersects line n at point B. What is the measure, in degrees, of the acute angle formed at point B?
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Why B is right
When a transversal intersects two parallel lines, corresponding angles are congruent and alternate interior angles are congruent. Since line p intersects both parallel lines m and n, the acute angle at point B is an alternate interior angle to the 65° angle at point A, so it also measures 65°.
Why the others are wrong
AThis is the result of incorrectly finding the complement of 65° (90° - 65° = 25°) instead of recognizing that alternate interior angles are equal.
CThis incorrectly adds values instead of recognizing the angle relationship between parallel lines.
DThis is the supplement of 65° (180° - 65° = 115°), but the question asks for the acute angle, not the obtuse supplementary angle at point B.
Question 2Medium
In triangle DEF, angle D measures 37°. The measure of angle E is twice the measure of angle F. What is the value of angle E?
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Why C is right
Let angle F equal x. Then angle E equals 2x. The sum of angles in triangle DEF is 180°, so 37° plus x plus 2x equals 180°. This gives 37° plus 3x equals 180°, so 3x equals 143°, and x equals 47.67°. Therefore, angle E equals 2 times 47.67°, which is 95.33°.
Why the others are wrong
AThis is the value of angle F, not angle E, resulting from stopping the calculation before applying the 2x relationship.
BThis results from incorrectly finding the supplement of some intermediate calculation or misapplying the 2:1 ratio.
DThis incorrectly assumes angle E equals angle D due to some vertical or symmetry property that does not apply.
Question 3Medium
Triangle GHI has angles measuring 44°, 71°, and 65°. Triangle JKL is similar to triangle GHI, where vertices G, H, and I correspond to vertices J, K, and L, respectively. What is the measure of angle K?
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Why D is right
Corresponding angles in similar triangles are congruent. Since vertex H in triangle GHI corresponds to vertex K in triangle JKL, angle K has the same measure as angle H. Therefore, angle K measures 71°.
Why the others are wrong
AThis incorrectly identifies angle K with the non-corresponding angle G rather than the corresponding angle H.
BThis incorrectly adds two of the angle measures instead of identifying the corresponding angle.
CThis incorrectly applies a complementary or supplementary calculation that is not relevant to similar triangles.
Question 4Medium
Lines j and k are parallel, and line m intersects both. At the intersection with line j, an angle of 156° is formed on one side of line m. What is the value of the acute angle formed on the same side of line m at the intersection with line k?
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Why A is right
The 156° angle and the acute angle at line j are supplementary, so the acute angle at line j=180° - 156° = 24°. Since same-side interior angles with parallel lines are supplementary, and the angle at line k is supplementary to 156°, the acute angle at line k is also 24°.
Why the others are wrong
BThis incorrectly treats the angles as complementary rather than finding the supplement of 156°.
CThis incorrectly applies vertical angle reasoning without properly accounting for the supplementary relationship.
DThis incorrectly assumes the angles are equal rather than recognizing the need to find the supplement first.
Question 5Medium
In the xy-plane, line k passes through points (2, 5) and (8, 11). Line m is perpendicular to line k. If line m passes through the point (4, 9), at what y-coordinate does line m intersect the y-axis?
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Why A is right
The slope of line k is (11 - 5) / (8 - 2) = 1. A perpendicular line has slope -1. Line m passes through (4, 9) with slope -1, so its equation is y−9=−1(x−4), or y=−x+13. At the y-axis (x=0), y=13.
Why the others are wrong
BThis incorrectly uses the y-coordinate from the first point on line k rather than computing the y-intercept of line m.
CThis incorrectly adds 4 and 13 instead of substituting x = 0 into the equation of line m.
DThis results from an error in calculating the perpendicular slope or in forming the equation of line m.
Question 6Medium
In the xy-plane, line m is parallel to line n. Line p intersects line m at point A, where angle 1 is formed measuring 118°. Line p intersects line n at point B, where angle 2 is formed on the same side of line p as angle 1. What is the value of angle 2?
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Why B is right
When parallel lines are cut by a transversal, corresponding angles are equal. Since line m is parallel to line n and line p is the transversal, angle 1 and angle 2 are corresponding angles on the same side of the transversal. Therefore, angle 2 measures 118°.
Why the others are wrong
AThis is the result of incorrectly finding the supplement of 118° by subtracting from 180°, which would apply to angles on a straight line rather than corresponding angles.
CThis incorrectly assumes the angles formed are vertical angles or applies an irrelevant perpendicular relationship.
DThis results from incorrectly adding 118° and some assumed angle measure rather than recognizing the corresponding angle relationship.
Question 7Medium
In triangle PQR, the measure of angle P is twice the measure of angle Q. If angle R measures 80°, what is the measure, in degrees, of angle Q?
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Why D is right
Let angle Q measure x degrees. Then angle P measures 2x degrees. The sum of angles is 180°, so x+2x+80° = 180°. Solving gives 3x=100°, so x=33.33° (or 100/3 degrees).
Why the others are wrong
AThis incorrectly divides 100° by 2, confusing the relationship between the angles.
BThis incorrectly computes 80° - 40° or uses 40° as if it were a complement of 50°.
CThis incorrectly finds 180° - 80° = 100° and assigns it to angle Q without accounting for the 2:1 ratio.
Question 8Medium
In triangle DEF, the measure of an exterior angle at vertex F is 135 degrees. If the measure of angle D is 68 degrees, what is the measure of angle E, in degrees?
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Why B is right
An exterior angle of a triangle equals the sum of the two remote interior angles. Therefore, angle D plus angle E equals 135 degrees, so angle E=135−68=67 degrees.
Why the others are wrong
AThis results from incorrectly using complementary angle relationships rather than the exterior angle theorem.
CThis results from incorrectly assuming angle E equals angle D through a vertical or alternate interior angle relationship that does not apply here.
DThis results from adding 135 and 68 rather than subtracting.
Question 9Medium
Lines a and b are parallel. Line c intersects line a, creating an angle that measures 143°. Line c also intersects line b. What is the measure, in degrees, of the acute angle formed where line c intersects line b?
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Why A is right
The 143° angle at line a and the acute angle at the same intersection point are supplementary, so the acute angle at line a measures 180° - 143° = 37°. Since lines a and b are parallel and line c is a transversal, corresponding angles are equal, so the acute angle at line b also measures 37°.
Why the others are wrong
BThis is the result of incorrectly finding the complement of 37° (90° - 37° = 53°) after one correct step.
CThis incorrectly adds unrelated angle measures rather than using the supplementary relationship and parallel line properties.
DThis incorrectly uses the obtuse angle measure directly, failing to recognize that the question asks for the acute angle.
Question 10Medium
Two parallel lines are cut by a transversal. One of the angles formed measures 43°. Another angle, which is an alternate interior angle to the first, forms part of a triangle with two other angles. If one of the other angles in this triangle measures 89°, what is the value of the third angle in the triangle?
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Why A is right
Alternate interior angles formed by parallel lines and a transversal are equal, so one angle of the triangle is 43°. The sum of angles in a triangle is 180°. With two angles measuring 43° and 89°, their sum is 132°. The third angle equals 180° minus 132°, which is 48°.
Why the others are wrong
BThis results from incorrectly finding the supplement of 43° by subtracting from 180° rather than using the triangle angle sum.
CThis incorrectly assumes the third angle equals the first angle due to some vertical or alternate angle property that does not apply within the triangle.
DThis results from incorrectly adding 43° and 89° rather than subtracting their sum from 180°.
Question 11Medium
Two parallel lines are cut by a transversal. One of the angles formed measures 118°. What is the measure, in degrees, of one of the acute angles formed by the transversal?
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Why B is right
When a transversal cuts two parallel lines, consecutive angles on the same side are supplementary. The acute angle and the 118° angle are supplementary, so the acute angle measures 180 - 118 = 62°.
CThis incorrectly assumes the acute angle equals the given obtuse angle, confusing vertical angles with supplementary angles.
DThis incorrectly adds 118° + 118° + 6° instead of subtracting from 180°.
Question 12Medium
Line j is parallel to line k. Line m intersects line j at point X, forming a 58° angle. Line m intersects line k at point Y. What is the measure, in degrees, of the obtuse angle formed at point Y?
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Why D is right
When a transversal intersects two parallel lines, alternate interior angles are equal. The 58° angle at point X and an acute angle at point Y are alternate interior angles, so that acute angle also measures 58°. The obtuse angle at point Y is supplementary to this, so it measures 180° - 58° = 122°.
Why the others are wrong
AThis is the result of incorrectly finding the complement of 58° (90° - 58° = 32°) rather than the supplement.
BThis gives the measure of the acute angle at point Y, not the obtuse angle requested.
CThis incorrectly assumes perpendicularity or adds unrelated values instead of using the supplementary angle relationship.
Question 13Medium
In triangle ABC, the measure of angle A is 62°. The measure of angle B is 3 times the measure of angle C. What is the measure, in degrees, of angle B?
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Why D is right
The sum of the measures of the interior angles of a triangle is 180°. Let the measure of angle C be x. Then angle B is 3x. The equation is 62+3x+x=180, which simplifies to 4x=118, so x=29.5. Therefore, angle B=3(29.5) = 88.5°.
Why the others are wrong
AThis is the result of incorrectly using 180 - 62 = 118 as a supplementary angle and then dividing by a factor.
BThis is the result of adding 62 and some fraction instead of using the constraint that angles sum to 180°.
CThis is 62 - 3, treating the relationship as vertical angles rather than applying the triangle angle sum.
Question 14Medium
Two parallel lines are cut by a transversal, forming eight angles. One of the angles measures 156°. What is the measure, in degrees, of one of the acute angles formed?
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Why A is right
When a transversal cuts two parallel lines, consecutive angles are supplementary. The acute angle and the 156° angle are supplementary, so the acute angle measures 180 - 156 = 24°.
Why the others are wrong
BThis incorrectly calculates the complement of 24° (90 - 24 = 66) instead of finding the supplement of 156°.
CThis incorrectly assumes the acute angle equals the given obtuse angle, confusing vertical or corresponding angles with supplementary angles.
DThis incorrectly doubles 156° instead of subtracting it from 180°.
Question 15Medium
Lines r and s are parallel. A transversal line t intersects line r, forming an angle of 112° on one side. Line t also intersects line s. What is the measure, in degrees, of the acute angle formed where line t intersects line s?
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Why B is right
The 112° angle and the acute angle on the same side of the transversal at line r are supplementary, so the acute angle at line r measures 180° - 112° = 68°. Since lines r and s are parallel, corresponding angles are equal, so the acute angle at line s also measures 68°.
Why the others are wrong
AThis incorrectly finds the complement of 68° (90° - 68° = 22°) after one correct step, rather than recognizing that 68° is the answer.
CThis incorrectly uses the obtuse angle measure directly, failing to recognize that the question asks for the acute angle.
DThis incorrectly adds values (112° + 34°) rather than recognizing the supplementary relationship.
Question 16Medium
Line j is parallel to line k. A transversal intersects both lines, forming angle 1 measuring 64° with line j. On line k, the transversal forms angle 2, which is supplementary to the corresponding angle of angle 1. What is the value of angle 2?
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Why D is right
When parallel lines are cut by a transversal, corresponding angles are equal. The corresponding angle to angle 1 on line k also measures 64°. Since angle 2 is supplementary to this corresponding angle, angle 2 equals 180° minus 64°, which is 116°.
Why the others are wrong
AThis incorrectly assumes angle 2 equals angle 1 due to vertical or corresponding angle properties without recognizing the supplementary relationship.
BThis results from incorrectly finding the complement of 64° by subtracting from 90° rather than the supplement from 180°.
CThis incorrectly adds 64° and 116° rather than recognizing that angle 2 is a single angle measuring the supplement.
Question 17Medium
In triangle DEF, the measure of angle D is 35 degrees. An exterior angle at vertex E measures 103 degrees. What is the measure, in degrees, of angle F?
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Why B is right
An exterior angle of a triangle equals the sum of the two remote interior angles. The exterior angle at E measures 103 degrees, so angle D plus angle F equals 103 degrees. Since angle D measures 35 degrees, angle F measures 103 - 35 = 68 degrees.
Why the others are wrong
AThis incorrectly uses the supplement of 103 (which is 77) and then subtracts 35, rather than directly applying the exterior angle theorem.
CThis is the supplement of 103 degrees, treating the exterior angle as if it needed to be converted to its supplementary angle before use.
DThis incorrectly adds 103 and 35 instead of subtracting to find the remote interior angle.
Question 18Medium
In triangle ABC, angle A measures 62 degrees and angle B measures 71 degrees. What is the measure, in degrees, of angle C?
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Why B is right
The sum of the interior angles of a triangle is 180 degrees. Since angle A measures 62 degrees and angle B measures 71 degrees, their sum is 133 degrees. Therefore, angle C measures 180 - 133 = 47 degrees.
Why the others are wrong
AThis is the result of incorrectly treating 62 and 71 as complementary angles (summing to 90) and subtracting from 180, rather than recognizing that all three angles sum to 180.
CThis incorrectly applies the vertical angle relationship or uses 71 as if it were an exterior angle, when the problem asks for an interior angle of the triangle.
DThis is the sum of angles A and B rather than the difference needed to find the third angle of the triangle.
Question 19Medium
In triangle DEF, an exterior angle at vertex F measures 132°. If the measure of angle D is 67°, what is the measure of angle E, in degrees?
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Why D is right
An exterior angle of a triangle equals the sum of the two remote interior angles. The exterior angle at F is 132°, so angle D + angle E=132°. Given angle D=67°, angle E=132° - 67° = 65°.
Why the others are wrong
AThis incorrectly computes 180° - 132°, treating the exterior angle as supplementary to angle E rather than using the exterior angle theorem.
BThis incorrectly adds 132° and 67° instead of subtracting to find the remaining remote interior angle.
CThis incorrectly assumes angle E equals angle D, perhaps confusing the triangle properties or misidentifying which angles are remote interior angles.
Question 20Medium
Two parallel lines are cut by a transversal. One angle measures 73 degrees. Another angle, which is a corresponding angle to a supplementary angle of the first, measures y degrees. What is the value of y?
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Why C is right
The supplementary angle to 73 degrees is 180 - 73 = 107 degrees. When parallel lines are cut by a transversal, corresponding angles are equal. Therefore, the corresponding angle to this 107-degree angle also measures 107 degrees.
Why the others are wrong
AThis incorrectly treats 73 and y as complementary (summing to 90) rather than applying the supplementary-then-corresponding transformation.
BThis skips the supplementary transformation and directly uses 73 as if corresponding angles were being compared to the original angle.
DThis incorrectly adds 73 and 107 instead of recognizing that y equals the corresponding angle to 107.
What to do after medium
Medium is the tier that decides most scores. If these are landing, the hard set is where the remaining points are.
Questions are written by SAT Climb and drawn from its own item bank. SAT® is a registered trademark of College Board, which is not affiliated with and does not endorse SAT Climb.