Question

the sum of the interior angle measures of a triangle must be 180°. so, ( mangle1 + mangle3 + mangle4 = 180° ). we are given that ( mangle1 = 78° ). so, ( mangle3 + mangle4 = 102° ). from the figure, we can see that ( mangle1 + mangle2 = 180° ). since ( mangle1 = 78° ), it must be that ( mangle2 = square° ). therefore, ( mangle2 ) select ( mangle3 + mangle4 ). this result is an example of the exterior angle property of triangles. for any triangle, the measure of an exterior angle select

Explanation:

Step1: Use the linear pair property

We know that \( m\angle1 + m\angle2 = 180^\circ \) (linear pair of angles are supplementary) and \( m\angle1 = 78^\circ \).

Step2: Solve for \( m\angle2 \)

Substitute \( m\angle1 = 78^\circ \) into the equation \( m\angle1 + m\angle2 = 180^\circ \).
So, \( 78^\circ + m\angle2 = 180^\circ \).
Subtract \( 78^\circ \) from both sides: \( m\angle2 = 180^\circ - 78^\circ = 102^\circ \).

Step3: Compare \( m\angle2 \) with \( m\angle3 + m\angle4 \)

We found that \( m\angle3 + m\angle4 = 102^\circ \) and \( m\angle2 = 102^\circ \), so \( m\angle2 = m\angle3 + m\angle4 \).

Step4: Recall the Exterior Angle Property

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.

Answer:

• \( m\angle2=\boldsymbol{102}^\circ \)
• \( m\angle2 \) is equal to \( m\angle3 + m\angle4 \)
• The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.