Question

question 36 | module 7 practice test
complete the statements below.

the sum of the interior angle measures of a triangle must be □°.
so, $m\angle1 + m\angle3 + m\angle4 = \square^\circ$.
we are given that $m\angle1=70^\circ$.
so, $m\angle3 + m\angle4 = \square^\circ$.
from the figure, we can see that $m\angle1 + m\angle2 = \square^\circ$.
since $m\angle1=70^\circ$, it must be that $m\angle2 = \square^\circ$.

therefore, $m\angle2$ select $m\angle3 + m\angle4$.

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

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles of a triangle is $180^\circ$.
So, $m\angle 1 + m\angle 3 + m\angle 4 = 180^\circ$.

Step2: Substitute given angle value

Given $m\angle 1=70^\circ$, solve for $m\angle 3 + m\angle 4$.
$70^\circ + m\angle 3 + m\angle 4 = 180^\circ$
$m\angle 3 + m\angle 4 = 180^\circ - 70^\circ = 110^\circ$

Step3: Recall supplementary angle pair

$\angle 1$ and $\angle 2$ form a straight line, so they are supplementary.
$m\angle 1 + m\angle 2 = 180^\circ$

Step4: Calculate $m\angle 2$

Substitute $m\angle 1=70^\circ$ to find $m\angle 2$.
$70^\circ + m\angle 2 = 180^\circ$
$m\angle 2 = 180^\circ - 70^\circ = 110^\circ$

Step5: Compare values

Compare $m\angle 2$ and $m\angle 3 + m\angle 4$.
$m\angle 2 = 110^\circ$ and $m\angle 3 + m\angle 4 = 110^\circ$, so they are equal.

Answer:

The sum of the interior angle measures of a triangle must be $180^\circ$.
So, $m\angle 1 + m\angle 3 + m\angle 4 = 180^\circ$.
We are given that $m\angle 1=70^\circ$.
So, $m\angle 3 + m\angle 4 = 110^\circ$.
From the figure, we can see that $m\angle 1 + m\angle 2 = 180^\circ$.
Since $m\angle 1=70^\circ$, it must be that $m\angle 2 = 110^\circ$.
Therefore, $m\angle 2$ $\boldsymbol{=}$ $m\angle 3 + m\angle 4$.
For any triangle, the measure of an exterior angle equals the sum of the measures of its two non-adjacent interior angles.