Question

for the figure shown, find ( mangle1 ) and ( mangle2 ).
(the figure is not drawn to scale)
( mangle1 = 66^{circ} )

Explanation:

Step1: Find \(m\angle1\)

Use the exterior - angle theorem. The exterior - angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
For the triangle with angles \(30^{\circ}\), \(36^{\circ}\), and \(\angle1\) (where \(\angle1\) is an exterior angle), we have \(m\angle1=30^{\circ}+36^{\circ}\)
\(m\angle1 = 66^{\circ}\)

Step2: Find \(m\angle2\)

Use the angle - sum property of a straight line. The sum of angles on a straight line is \(180^{\circ}\).
We know that one of the angles on the straight line is \(96^{\circ}\) and \(m\angle2\) is adjacent to it. So, \(m\angle2+96^{\circ}=180^{\circ}\)
\(m\angle2=180^{\circ}-96^{\circ}\)
\(m\angle2 = 84^{\circ}\)

Answer:

\(m\angle1 = 66^{\circ}\), \(m\angle2=84^{\circ}\)