Question

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Explanation:

Step1: Find interior - angles adjacent to 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: Find the third interior - angle of the triangle

Let the third interior - angle of the triangle be \(x\). Using the angle - sum property of a triangle (\(x + 68+54 = 180\)), we get \(x=180-(68 + 54)=58^{\circ}\).

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 \(m=68 + 58=126^{\circ}\) (exterior - angle property of a triangle).

Answer:

\(126\)