NJSLA Geometric Principles and Measurement 4

Question 1

An exterior angle of a triangle measures 130°. One of the non-adjacent interior angles measures 75°. What is the other non-adjacent interior angle?

Accepted Answer

55°

Answer

An exterior angle equals the sum of the two non-adjacent interior angles: 130° = 75° + x, so x = 55°.

Question 2

A rectangular prism has dimensions 4 cm × 6 cm × 9 cm. What is its total surface area?

Accepted Answer

228 cm²

Answer

SA = 2(lw + lh + wh) = 2(24 + 36 + 54) = 2(114) = 228 cm².

Question 3

Point M is the midpoint of segment PQ. P is at (−4, 2) and M is at (1, 5). What are the coordinates of Q?

Accepted Answer

(6, 8)

Answer

Using midpoint formula: 1 = (−4 + x)/2 → x = 6; 5 = (2 + y)/2 → y = 8, so Q = (6, 8).

Question 4

Two supplementary angles are in the ratio 2:7. What are their measures?

Accepted Answer

40° and 140°

Answer

2x + 7x = 180°, so 9x = 180°, x = 20°; the angles are 40° and 140°.

Question 5

A sphere has a diameter of 12 cm. What is its volume? (Use π ≈ 3.14)

Accepted Answer

904.32 cm³

Answer

Radius = 6 cm; V = (4/3)πr³ = (4/3)(3.14)(216) = 904.32 cm³.

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