Question

26,394 Learners found this answer helpful

in the figure below, suppose ( mangle 2 = 30^{circ} ) and ( mangle 3 = 66^{circ} ).

complete the statements below.

the sum of the interior angle measures of a triangle must be ( square^{circ} ).
so, ( mangle 2 + mangle 3 + mangle 4 = square^{circ} ).

we are given that ( mangle 2 = 30^{circ} ).
so, ( mangle 3 + mangle 4 = square^{circ} ).

from the figure, we can see that ( mangle 1 + mangle 2 = square^{circ} ).
since ( mangle 2 = 30^{circ} ), it must be that ( mangle 1 = square^{circ} ).

therefore, ( mangle 1 ) select ( mangle 3 + mangle 4 ).

this result is an example of the exterior angle property of triangles.
for any triangle, the measure of an exterior angle
select

Explanation:

Step1: Triangle interior angle sum

The sum of interior angles of a triangle is \(180^{\circ}\). So \(m\angle2 + m\angle3 + m\angle4=180^{\circ}\).

Step2: Calculate \(m\angle3 + m\angle4\)

Given \(m\angle2 = 30^{\circ}\), then \(m\angle3 + m\angle4=180 - 30=150^{\circ}\).

Step3: Straight - angle property

\(\angle1\) and \(\angle2\) form a straight angle (\(180^{\circ}\)). So \(m\angle1 + m\angle2 = 180^{\circ}\).

Step4: Calculate \(m\angle1\)

Since \(m\angle2 = 30^{\circ}\), then \(m\angle1=180 - 30 = 150^{\circ}\).

Answer:

The sum of the interior angle measures of a triangle must be \(180^{\circ}\). So, \(m\angle2 + m\angle3 + m\angle4 = 180^{\circ}\). We are given that \(m\angle2 = 30^{\circ}\). So, \(m\angle3 + m\angle4 = 150^{\circ}\). From the figure, we can see that \(m\angle1 + m\angle2 = 180^{\circ}\). Since \(m\angle2 = 30^{\circ}\), it must be that \(m\angle1 = 150^{\circ}\). Therefore, \(m\angle1=\) \(m\angle3 + m\angle4\). For any triangle, the measure of an exterior angle is equal to the sum of the measures of the two non - adjacent interior angles.