Question

1. which of the following is a true statement about the angles in the figure below?

a. the $m\angle3$ is $142^\circ$.
b. the $m\angle1$ is $99^\circ$.
c. the $m\angle2$ is $137^\circ$.
d. the $m\angle4$ is $137^\circ$.

Explanation:

Step1: Calculate $m\angle1$

Sum of triangle angles is $180^\circ$.
$m\angle1 = 180^\circ - 43^\circ - 56^\circ = 81^\circ$

Step2: Calculate $m\angle3$

$\angle3$ and $56^\circ$ are supplementary.
$m\angle3 = 180^\circ - 56^\circ = 124^\circ$

Step3: Calculate $m\angle2$

$\angle2$ and $\angle1$ are supplementary.
$m\angle2 = 180^\circ - 81^\circ = 99^\circ$

Step4: Calculate $m\angle4$

$\angle4$ and $43^\circ$ are supplementary.
$m\angle4 = 180^\circ - 43^\circ = 137^\circ$

Step5: Match with options

Compare calculated values to given choices.

Answer:

D. The m∠4 is 137°.