Geometry

Question Analysis

This question focuses on using angle relationships to find the measure of ∠1. The main task is to correctly apply the properties related to the identified linear - angle (linear - pair) relationship.

 

Key Concept Explanation

A linear pair of angles consists of two adjacent angles that share a common vertex and a common side, with their non - common sides forming a straight line. The sum of the measures of angles in a linear pair is 180°.

 

Step - by - Step Solution

1. Since ∠1 and the 112° angle form a linear pair:

According to the property of a linear pair, we know that m∠1 + 112°= 180°.

To find m∠1, we solve the equation for ∠1. Subtract 112° from both sides of the equation: m∠1=180° - 112°.

Performing the subtraction, 180° - 112° = 68°. So, m∠1 = 68°.

 

Common Mistakes

Forgetting the 180° sum property of a ...