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 larger triangle, if we consider the exterior angle of measure \(127^{\circ}\), and the two non - adjacent interior angles are \(32^{\circ}\) and \(\angle1\). So, \(m\angle1+32^{\circ}=127^{\circ}\).
\[m\angle1 = 127^{\circ}-32^{\circ}\]
\[m\angle1=95^{\circ}\]

Step2: Use linear - pair property

\(\angle1\) and \(\angle2\) form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\). Since \(m\angle1 = 95^{\circ}\), then \(m\angle2=180^{\circ}-m\angle1\).
\[m\angle2=180^{\circ}-95^{\circ}\]
\[m\angle2 = 85^{\circ}\]

Answer:

\(m\angle1 = 95^{\circ}\), \(m\angle2 = 85^{\circ}\)