Question

for the figure shown, find m∠1 and m∠2. m∠1 = 117° m∠2 = □° (the figure is not drawn to scale)

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the larger triangle, the exterior angle of measure \(117^{\circ}\) is equal to the sum of the two non - adjacent interior angles. Let's assume the two non - adjacent interior angles of the larger triangle are \(x\) and \(y\). For the smaller triangle, we know that one of its exterior angles is related to \(\angle2\).
We first note that the angle adjacent to \(117^{\circ}\) is \(180 - 117=63^{\circ}\).

Step2: Find \(\angle2\)

In the smaller triangle, we know that the exterior angle of the smaller triangle (the angle formed by extending one of its sides) is related to \(\angle2\). Since the sum of angles in a triangle is \(180^{\circ}\), and considering the relationships between the angles in the figure. The angle adjacent to \(117^{\circ}\) and the other two angles in the smaller triangle are related.
We know that \(\angle2 = 117 - 15=102^{\circ}\)

Answer:

\(m\angle2 = 102^{\circ}\)