Question

what is m∠1? m∠1 =

Explanation:

Step1: Find the adjacent - interior angle to 105°

The adjacent - interior angle to the 105° exterior angle and the 105° angle form a linear pair. The sum of angles in a linear pair is 180°. So the adjacent - interior angle is \(180 - 105=75^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the three interior angles of the triangle be \(m\angle1\), 68°, and 75°. Then \(m\angle1+68 + 75=180\).
We can solve for \(m\angle1\) as \(m\angle1=180-(68 + 75)\).
First, calculate \(68 + 75 = 143\). Then \(m\angle1=180 - 143=37^{\circ}\).

Answer:

37