Apply angle relationships and triangle properties, including similarity, to solve for unknown measures.
86 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 96° and 31°. What is the measure of the third angle?
The angles of a triangle sum to 180°, so the third angle = 180° − 96° − 31° = 53°.
In a triangle, two of the angles measure 87° and 34°. What is the measure of the third angle?
The angles of a triangle sum to 180°, so the third angle = 180° − 87° − 34° = 59°.
In a triangle, two of the angles measure 33° and 97°. What is the measure of the third angle?
The angles of a triangle sum to 180°, so the third angle = 180° − 33° − 97° = 50°.
In a triangle, two of the angles measure 35° and 39°. What is the measure of the third angle?
The angles of a triangle sum to 180°, so the third angle = 180° − 35° − 39° = 106°.