Lines, Angles, and Triangles Flashcards

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

Answer: 100°

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

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

Answer: 19

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

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?

Answer: 128 cm²

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

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?

Answer: 5°

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

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

Answer: 110°

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

Parallel lines are cut by a transversal. The co-interior angles are (6n − 10)° and (4n + 30)°. What is n?

Answer: 16

Co-interior angles sum to 180°: (6n−10)+(4n+30)=180 → 10n+20=180 → n=16.

In a triangle, the largest angle is 4 times the smallest. If the third angle is 60°, what is the largest angle?

Answer: 96°

Let smallest = x; largest = 4x; x + 4x + 60 = 180 → 5x = 120 → x = 24; largest = 96°.