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 in geometry for solving problems related to angle measures.

 

Step-by-Step Solution

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

2. Given that the measure of ∠E is 46°. Substitute the value of ∠E into the equation: 46°+ ∠F = 180°.

3. To find the measure of ∠F, we subtract 46° from both sides of the equation: ∠F=180° - 46° = 134°.

 

Option Analysis

A.44°: Incorrect. If ∠F = 44°, then ∠E+∠F = 46° + 44°=90°, which means they are complementary, not supplementary.

B.54°: Incorrect. Since 46°+54° = 100°≠180°.

C.144°: Incorrect. As 46°+144° = 1...