Bluebook SAT Test Lines, Angles, and Triangles 9

Question 1

In triangle ABC, side AB = 7, BC = 24, and angle B = 90°. What is the length of AC?

Accepted Answer

25

Answer

AC = √(AB² + BC²) = √(49 + 576) = √625 = 25.

Question 2

Two angles of a triangle are 54° and 78°. A line is drawn from the third vertex perpendicular to the opposite side. What is the measure of the third angle of the triangle?

Accepted Answer

48°

Answer

Third angle = 180° − 54° − 78° = 48°.

Question 3

Parallel lines r and s are cut by a transversal. A co-interior angle on line r measures (6x + 5)° and the co-interior angle on line s measures (4x + 15)°. What is x?

Accepted Answer

16

Answer

Co-interior angles are supplementary: (6x+5)+(4x+15) = 180 → 10x+20 = 180 → x = 16.

Question 4

An angle bisector divides a 136° angle into two equal parts. What is the measure of each part?

Accepted Answer

68°

Answer

Each part = 136° / 2 = 68°.

Question 5

Triangle XYZ is similar to triangle PQR. If XY = 12, YZ = 16, and PQ = 9, what is QR?

Accepted Answer

12

Answer

Ratio = PQ/XY = 9/12 = 3/4; QR = YZ × 3/4 = 16 × 3/4 = 12.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Lines, Angles, and Triangles 9