Lines, Angles, and Triangles Flashcards

Point P is inside triangle ABC such that angle PBC = 20° and angle PCB = 30°. If angle BAC = 70°, what is angle BPC?

Answer: 130°

In triangle BPC: angle BPC = 180° − 20° − 30° = 130°.

A transversal crosses parallel lines forming co-interior angles of (5y − 10)° and (3y + 30)°. What is y?

Answer: 20

Co-interior angles sum to 180°: (5y−10)+(3y+30)=180 → 8y+20=180 → y=20.

Triangle ABC has angles A = (x + 20)°, B = (2x − 5)°, and C = (x + 45)°. What is angle B?

Answer: 55°

Sum = 180°: (x+20)+(2x−5)+(x+45) = 180 → 4x+60 = 180 → x = 30; B = 2(30)−5 = 55°.

Two straight lines intersect. One pair of vertical angles is (3k + 7)° and (k + 43)°. What is k?

Answer: 18

Vertical angles are equal: 3k+7 = k+43 → 2k = 36 → k = 18.

In triangle DEF, DE is the longest side. Which angle must be the largest?

Answer: Angle F

The largest angle is opposite the longest side; DE is opposite angle F.

Parallel lines a and b are cut by transversal t. The angle at the intersection with a is 148°. What is the size of the alternate exterior angle at b?

Answer: 148°

Alternate exterior angles are equal when lines are parallel, so the angle is 148°.

A straight angle is divided into three consecutive angles: x, 2x, and 3x. What is the measure of the middle angle?

Answer: 60°

x + 2x + 3x = 180° → 6x = 180° → x = 30°; middle angle = 2x = 60°.