Apply angle relationships and triangle properties, including similarity, to solve for unknown measures.
38 original lines, angles, and triangles questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
Triangle ABC is similar to triangle DEF. If AB = 6, BC = 9, and DE = 8, what is EF?
The similarity ratio is AB:DE = 6:8 = 3:4, so BC:EF must also be 3:4. EF = 9 × (4/3) = 12.
In a triangle, two of the angles measure 43° and 58°. What is the measure of the third angle?
The angles of a triangle sum to 180°, so the third angle is 180° − 43° − 58° = 79°. Choice 101° is the supplement of the sum of the two given angles, not the third angle.
Two parallel lines are cut by a transversal. One of the interior angles measures 118°. What is the measure of the interior angle on the same side of the transversal?
Interior angles on the same side of a transversal between parallel lines are supplementary, so the other measures 180° - 118° = 62°. Choice 118° would be the alternate interior angle, which is equal rather than supplementary.
Triangle ABC is similar to triangle DEF, with AB corresponding to DE. If AB = 6, BC = 8, and DE = 9, what is the length of EF?
The scale factor is DE/AB = 9/6 = 1.5, and corresponding sides scale by the same factor, so EF = 8 × 1.5 = 12. Choice 10.5 comes from adding the difference of 3 rather than multiplying.
In isosceles triangle PQR, side PQ equals side PR and angle P measures 40°. What is the measure of angle Q?
The angles opposite the two equal sides are equal, so angles Q and R share the remaining 180° - 40° = 140°, giving 70° each. Choice 140° is the combined total rather than one angle.