Question

find the value of m. 126° 112° m°

Explanation:

Step1: Find interior angles adjacent to given exterior angles

The interior - angle adjacent to the 112° exterior angle is \(180 - 112=68^{\circ}\) (linear - pair of angles, sum is 180°). The interior - angle adjacent to the 126° exterior angle is \(180 - 126 = 54^{\circ}\) (linear - pair of angles, sum is 180°).

Step2: Use the angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let the third interior angle of the triangle be \(x\). So, \(x+68 + 54=180\), then \(x=180-(68 + 54)=58^{\circ}\).

Step3: Find the value of \(m\)

The angle \(m\) is an exterior angle of the triangle. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(m=68 + 54=122^{\circ}\) (exterior - angle property of a triangle).

Answer:

\(122^{\circ}\)