Question

1. it is known that ∠efg and ∠gfh are a linear - angle pair. if m∠efg = 146°, then which of the following is the measure of ∠gfh? (1) 34° (2) 73° (3) 106° (4) 146°

Explanation:

Step1: Recall linear - angle - pair property

The sum of angles in a linear - angle pair is 180°. So, \(m\angle EFG + m\angle GFH=180^{\circ}\).

Step2: Solve for \(m\angle GFH\)

Given \(m\angle EFG = 146^{\circ}\), we substitute into the equation: \(m\angle GFH=180^{\circ}-m\angle EFG\). Then \(m\angle GFH = 180 - 146=34^{\circ}\).

Answer:

(1) \(34^{\circ}\)