Question

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

Explanation:

Step1: Use angle - sum property of a triangle

In the smaller triangle with angles \(27^{\circ}\) and \(30^{\circ}\), the third - angle (let's call it \(x\)) inside this triangle is \(180-(27 + 30)=123^{\circ}\).

Step2: Use linear - pair property

\(\angle1\) and \(x\) form a linear pair. So \(m\angle1=180 - 123\).
\(m\angle1 = 57^{\circ}\)

Step3: Use vertical - angle property

\(\angle2\) and the angle with measure \(27^{\circ}+30^{\circ}=57^{\circ}\) are vertical angles. So \(m\angle2 = 57^{\circ}\)

Answer:

\(m\angle1 = 57^{\circ}\), \(m\angle2 = 57^{\circ}\)