Question

find the measure of the indicated angle.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In triangle GMN, if one angle is 34° and another is 71°.
Let the third - angle in triangle GMN be $\angle{GMN}=x$. Then $x + 34^{\circ}+71^{\circ}=180^{\circ}$.

Step2: Calculate the third - angle in triangle GMN

$x=180^{\circ}-(34^{\circ} + 71^{\circ})=180^{\circ}-105^{\circ}=75^{\circ}$.

Step3: Recall the property of a straight - line angle

The angle $\angle{GMN}$ and the unknown angle (let's call it $\theta$) form a straight - line. A straight - line angle is 180°.
So $\theta + 75^{\circ}=180^{\circ}$.

Step4: Calculate the unknown angle

$\theta=180^{\circ}-75^{\circ}=105^{\circ}$.

Answer:

$105$