Question

for the figure shown, find m∠1 and m∠2. m∠1 = 127°. 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 triangle with angle 1, if we consider the exterior - angle relationship, we know that \(m\angle1\) is the exterior angle of a triangle with interior angles 32° and 95°. So \(m\angle1=32^{\circ}+95^{\circ}=127^{\circ}\) (already given).

Step2: Use linear - pair property

\(\angle1\) and \(\angle2\) form a linear pair. A linear pair of angles is supplementary, that is, the sum of the measures of two angles in a linear pair is 180°. Let \(m\angle2=x\). Then \(m\angle1 + x=180^{\circ}\). Since \(m\angle1 = 127^{\circ}\), we have \(x=180^{\circ}-127^{\circ}\).
\[x = 53^{\circ}\]

Answer:

\(m\angle2 = 53^{\circ}\)