Question

if ( mangle1 + mangle3 = 150^circ ), what is ( mangle2 )?
note: figure is not drawn to scale.
a. ( 30^circ )
b. ( 152^circ )
c. ( 120^circ )
d. ( 33^circ )

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\), so \(m\angle1 + m\angle2 + m\angle3 = 180^\circ\).

Step2: Substitute known sum

We know \(m\angle1 + m\angle3 = 150^\circ\). Substitute into the angle - sum formula: \(150^\circ+m\angle2 = 180^\circ\).

Step3: Solve for \(m\angle2\)

Subtract \(150^\circ\) from both sides: \(m\angle2=180^\circ - 150^\circ=30^\circ\).

Answer:

A. \(30^\circ\)