Question

question 36 · module 7 practice test
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estion 36 | module 7 practice test
the figure below, suppose $m\angle1=34^\circ$ and $m\angle3=33^\circ$.
complete the statements below.
the sum of the interior angle measures of a triangle must be $\square^\circ$.
so, $m\angle1 + m\angle2 + m\angle3 = \square^\circ$.
we are given that $m\angle3=33^\circ$.
so, $m\angle1 + m\angle2 = \square^\circ$.
from the figure, we can see that $m\angle3 + m\angle4 = \square^\circ$.
since $m\angle3=33^\circ$, it must be that $m\angle4 = \square^\circ$.
therefore, $m\angle4$ select $m\angle1 + m\angle2$.

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles of a triangle is $180^\circ$.

Step2: Calculate $\angle1+\angle2+\angle3$

Substitute the known rule:
$m\angle1 + m\angle2 + m\angle3 = 180^\circ$

Step3: Solve for $\angle1+\angle2$

Substitute $m\angle3=33^\circ$:
$m\angle1 + m\angle2 = 180^\circ - 33^\circ = 147^\circ$

Step4: Identify linear pair sum

$\angle3$ and $\angle4$ form a linear pair, so their sum is $180^\circ$.

Step5: Calculate $m\angle4$

Substitute $m\angle3=33^\circ$:
$m\angle4 = 180^\circ - 33^\circ = 147^\circ$

Step6: Compare $m\angle4$ and $\angle1+\angle2$

Both equal $147^\circ$, so they are equal.

Answer:

The sum of the interior angle measures of a triangle must be $\boldsymbol{180}^\circ$.
So, $m\angle1 + m\angle2 + m\angle3 = \boldsymbol{180}^\circ$.
We are given that $m\angle3=33^\circ$.
So, $m\angle1 + m\angle2 = \boldsymbol{147}^\circ$.
From the figure, we can see that $m\angle3 + m\angle4 = \boldsymbol{180}^\circ$.
Since $m\angle3=33^\circ$, it must be that $m\angle4 = \boldsymbol{147}^\circ$.
Therefore, $m\angle4$ $\boldsymbol{=}$ $m\angle1 + m\angle2$.