Bluebook SAT Test Lines, Angles, and Triangles 15

Question 1

In triangle ABC, the angle bisector from A meets BC at D. If angle BAC = 80° and angle ABC = 60°, what is angle ADB?

Accepted Answer

100°

Answer

Angle BAD = 40° (half of 80°); in triangle ABD: angle ADB = 180° − 40° − 60° = 80°.

Question 2

Two angles are complementary. One is (3x + 5)° and the other is (x + 9)°. What is x?

Accepted Answer

19

Answer

Complementary angles sum to 90°: (3x+5)+(x+9)=90 → 4x+14=90 → x=19.

Question 3

Triangles PQR and STU are similar with a ratio of 5:8. The area of triangle PQR is 50 cm². What is the area of triangle STU?

Accepted Answer

128 cm²

Answer

Area ratio = (5/8)² = 25/64; area STU = 50 × (64/25) = 128 cm².

Question 4

A point P is on line segment AB (between A and B). Rays PX and PY are on opposite sides of AB. If angle APX = 135° and angle BPY = 40°, what is angle XPY?

Accepted Answer

5°

Answer

Angles on a straight line at P: 135° + angle XPB = 180° → angle XPB = 45°; angle XPY = angle XPB − angle BPY = 45° − 40° = 5°.

Question 5

In isosceles triangle ABC, AB = BC and angle BAC = (2m + 5)° and angle BCA = (3m − 10)°. What is angle ABC?

Accepted Answer

110°

Answer

Setting base angles equal: 2m+5 = 3m−10 → m = 15; each base angle = 35°; angle ABC = 180° − 70° = 110°.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Lines, Angles, and Triangles 15