Geometry

Question Analysis

This question involves the concept of supplementary angles.

 

Key Concept Explanation

Supplementary angles are two angles whose sum is 180°. This relationship is fundamental for solving angle - measurement problems in geometry.

 

Step-by-Step Solution

1. We know that ∠P and ∠Q are supplementary, so the equation is ∠P+∠Q = 180°.

2. Given that the measure of ∠P is 18°. Substitute the value of ∠P into the equation: 18°+∠Q = 180°.

3. To find the measure of ∠Q, we subtract 18° from both sides of the equation: ∠Q = 180° - 18° = 162°.

 

Option Analysis

A.82°: Incorrect. If ∠Q = 82°, then 18°+82° = 100°≠180°.

B.72°: Incorrect. Since 18°+72° = 90°, which means they are complementary, not supplementary.

C.162°: Correct. Because 18°+162° = 180°...