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SAT Math

Lines, Angles, and Triangles

Lines, Angles, and Triangles is a skill in the Geometry and Trigonometry domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.

11 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.

Round length
Difficulty (none selected means all)

Sample questions

Open a question to see the answer choices and the correct answer.

In triangle PQR, PQ = PR, and the measure of angle P is 48°. What is the measure of angle Q?
  1. A. 132°
  2. B. 24°
  3. C. 66° ✓
  4. D. 48°

Correct answer: C. Since PQ = PR, angles Q and R are the base angles of an isosceles triangle and are equal; they share the remaining 180° − 48° = 132° equally, so each measures 66°.

In a triangle, one exterior angle measures 118°. The triangle's two remote interior angles have measures y° and (y + 10)°. What is the value of y?
  1. A. 59
  2. B. 108
  3. C. 64
  4. D. 54 ✓

Correct answer: D. By the exterior angle theorem, an exterior angle equals the sum of the two remote interior angles, so y + (y + 10) = 118, which gives 2y = 108 and y = 54.

The three angles of a triangle measure 2x°, 3x°, and 4x°. What is the measure of the largest angle?
  1. A. 80° ✓
  2. B. 20°
  3. C. 90°
  4. D. 60°

Correct answer: A. The angles of a triangle sum to 180°, so 2x + 3x + 4x = 180, giving 9x = 180 and x = 20; the largest angle is 4x = 4(20) = 80°.

Two parallel lines are cut by a transversal. One same-side (co-interior) angle measures (2x + 15)° and the other measures (3x − 5)°. What is the measure of the angle labeled (3x − 5)°?
  1. A. 97° ✓
  2. B. 83°
  3. C. 34°
  4. D. 90°

Correct answer: A. Correct — same-side interior angles formed by a transversal across parallel lines are supplementary, so (2x + 15) + (3x − 5) = 180, giving 5x + 10 = 180, so x = 34; then 3(34) − 5 = 97°.

In triangle ABC, the exterior angle at vertex C measures (7x − 8)°. The two remote interior angles measure (2x + 10)° and (3x + 2)°. What is the measure of the interior angle at vertex C (adjacent to that exterior angle)?
  1. A. 62°
  2. B. 118° ✓
  3. C. 10°
  4. D. 32°

Correct answer: B. Correct — by the exterior angle theorem, 7x − 8 = (2x + 10) + (3x + 2), which gives 2x = 20, so x = 10; the exterior angle is 7(10) − 8 = 62°, and the interior angle at C is supplementary to it: 180 − 62 = 118°.