Bluebook SAT Test Lines, Angles, and Triangles 6

Question 1

Line l is parallel to line m. A transversal makes a 48° alternate interior angle with l. What is the corresponding alternate interior angle at m?

Accepted Answer

48°

Answer

Alternate interior angles formed by parallel lines are equal: 48°.

Question 2

A triangle has sides 7, 24, and 25. Is it a right triangle?

Accepted Answer

Yes, because 7² + 24² = 25²

Answer

7² + 24² = 49 + 576 = 625 = 25²; it satisfies the Pythagorean theorem.

Question 3

A linear pair of angles measures (3x + 15)° and (x + 25)°. What is x?

Accepted Answer

35

Answer

(3x+15)+(x+25)=180 → 4x+40=180 → x=35.

Question 4

Two similar triangles have perimeters 30 cm and 45 cm. A side of the smaller is 8 cm. What is the corresponding side of the larger?

Accepted Answer

12 cm

Answer

Ratio = 30:45 = 2:3; corresponding side = 8 × 3/2 = 12 cm.

Question 5

Triangle MNP has an exterior angle at M of 130°. Angle N = 70°. What is angle P?

Accepted Answer

60°

Answer

Exterior at M = angle N + angle P → 130° = 70° + P → P = 60°.

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