Question

in the figure below, suppose ( mangle1 = 79^{circ} ) and ( mangle2 = 44^{circ} ).

complete the statements below.

the sum of the interior angle measures of a triangle must be ( square^{circ} ).
so, ( mangle1 + mangle2 + mangle3=square^{circ} ).

we are given that ( mangle1 = 79^{circ} ) and ( mangle2 = 44^{circ} ).
therefore, ( mangle1 + mangle2=square^{circ} ).
and so ( mangle3=square^{circ} ).

from the figure, we can see that ( mangle3 + mangle4=square^{circ} ).
using the value we already found for ( mangle3 ), we find that ( mangle4=square^{circ} ).

therefore, ( mangle4 ) select ( mangle1 + mangle2 ).

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

Explanation:

Step1: Sum of interior angles of a triangle

The sum of the interior angle measures of a triangle must be \(180^{\circ}\). So, \(m\angle1 + m\angle2 + m\angle3=180^{\circ}\).

Step2: Calculate \(m\angle1 + m\angle2\)

We are given that \(m\angle1 = 79^{\circ}\) and \(m\angle2 = 44^{\circ}\). Then \(m\angle1 + m\angle2=79 + 44=123^{\circ}\).

Step3: Calculate \(m\angle3\)

Since \(m\angle1 + m\angle2 + m\angle3 = 180^{\circ}\), then \(m\angle3=180-(m\angle1 + m\angle2)=180 - 123 = 57^{\circ}\).

Step4: Relationship between \(\angle3\) and \(\angle4\)

From the figure, \(\angle3\) and \(\angle4\) are supplementary (form a linear - pair). So \(m\angle3 + m\angle4=180^{\circ}\).

Step5: Calculate \(m\angle4\)

Using \(m\angle3 = 57^{\circ}\), we get \(m\angle4=180 - m\angle3=180-57 = 123^{\circ}\).

Answer:

The sum of the interior angle measures of a triangle must be \(180^{\circ}\). So, \(m\angle1 + m\angle2 + m\angle3 = 180^{\circ}\). \(m\angle1 + m\angle2=123^{\circ}\). \(m\angle3 = 57^{\circ}\). \(m\angle3 + m\angle4 = 180^{\circ}\). \(m\angle4 = 123^{\circ}\). \(m\angle4=m\angle1 + m\angle2\). For any triangle, the measure of an exterior angle is equal to the sum of the measures of the two non - adjacent interior angles.