Bluebook SAT Test Lines, Angles, and Triangles 3

Question 1

A transversal intersects two parallel lines. The co-interior angles are (3x + 10)° and (2x + 30)°. What is x?

Accepted Answer

28

Answer

(3x+10)+(2x+30)=180 → 5x+40=180 → x=28.

Question 2

The angles of a triangle are in the ratio 2:3:7. What is the measure of the largest angle?

Accepted Answer

105°

Answer

2k+3k+7k=180° → k=15°; largest = 7×15° = 105°.

Question 3

An exterior angle of a triangle is 140°. One remote interior angle is 80°. What is the other?

Accepted Answer

60°

Answer

80° + x = 140° → x = 60°.

Question 4

Two lines intersect. Vertical angles are (5x − 10)° and (3x + 30)°. What is x?

Accepted Answer

20

Answer

5x − 10 = 3x + 30 → 2x = 40 → x = 20.

Question 5

An isosceles triangle has base angles of 65° each. What is the vertex angle?

Accepted Answer

50°

Answer

Vertex angle = 180° − 65° − 65° = 50°.

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