Bluebook SAT Test Lines, Angles, and Triangles 10

Question 1

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

Accepted Answer

130°

Answer

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

Question 2

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

Accepted Answer

20

Answer

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

Question 3

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

Accepted Answer

55°

Answer

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

Question 4

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

Accepted Answer

18

Answer

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

Question 5

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

Accepted Answer

Angle F

Answer

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

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