Question

part 2 of 2 for the figure shown, find m∠1 and m∠2. m∠1 = 118° m∠2 = (the figure is not drawn to scale.) due sep 24 - 11:45 pm

Explanation:

Step1: Use exterior - angle property of a triangle for ∠1

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the larger triangle, if the exterior angle is 134°, then \(m\angle1+84^{\circ}=134^{\circ}\).
So, \(m\angle1 = 134^{\circ}-84^{\circ}\).

Step2: Calculate the value of ∠1

\(m\angle1=50^{\circ}\)

Step3: Use exterior - angle property of a triangle for ∠2

For the smaller triangle, if one exterior angle is \(m\angle1 = 50^{\circ}\), and the non - adjacent interior angles are \(m\angle2\) and \(16^{\circ}\), then \(m\angle2 + 16^{\circ}=m\angle1\).
Since \(m\angle1 = 50^{\circ}\), we have \(m\angle2=50^{\circ}-16^{\circ}\).

Step4: Calculate the value of ∠2

\(m\angle2 = 34^{\circ}\)

Answer:

\(m\angle1 = 50^{\circ}\), \(m\angle2 = 34^{\circ}\)