which of the following is a true statement about the angles in the figure below?
the ( mangle 2 ) is ( 137^{circ} )
the ( mangle 1 ) is ( 99^{circ} )
the ( mangle 3 ) is ( 142^{circ} )
the ( mangle 4 ) is ( 137^{circ} )

Question

Accepted Answer

# Explanation:
## Step1: Find $m\angle1$
Use the triangle - angle sum theorem ($m\angle1 + 43^{\circ}+56^{\circ}=180^{\circ}$).
$$
\begin{align*}
m\angle1&=180^{\circ}-(43^{\circ} + 56^{\circ})\
&=180^{\circ}-99^{\circ}\
&=81^{\circ}
\end{align*}
$$
## Step2: Find $m\angle2$
Use the linear - pair relationship ($m\angle1+m\angle2 = 180^{\circ}$).
$$
\begin{align*}
m\angle2&=180^{\circ}-m\angle1\
&=180^{\circ}-81^{\circ}\
&=99^{\circ}
\end{align*}
$$
## Step3: Find $m\angle3$
Use the linear - pair relationship ($m\angle3+56^{\circ}=180^{\circ}$).
$$
\begin{align*}
m\angle3&=180^{\circ}-56^{\circ}\
&=124^{\circ}
\end{align*}
$$
## Step4: Find $m\angle4$
Use the linear - pair relationship ($m\angle4 + 43^{\circ}=180^{\circ}$).
$$
\begin{align*}
m\angle4&=180^{\circ}-43^{\circ}\
&=137^{\circ}
\end{align*}
$$

# Answer:
The $m\angle4$ is $137^{\circ}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find \(m\angle1\)

Step2: Find \(m\angle2\)

Step3: Find \(m\angle3\)

Step4: Find \(m\angle4\)

Answer: