Question

what is m∠2 + m∠3? explain.
a. 180; m∠1 + 90 = 180, so m∠2 + m∠3 = 180.
b. 180; m∠1 + 90 = m∠2 + m∠3, so m∠2 + m∠3 = 180.
c. 90; m∠1 + m∠2 + m∠3 = 180. m∠1 = 90, so m∠2 + m∠3 = 90.
d. 90; ∠2 and ∠3 are corresponding angles, so m∠2 + m∠3 = 90.

Explanation:

Step1: Identify angle - sum property

The sum of angles around a point on a straight - line is 180 degrees. In the given figure, $\angle1$, $\angle2$, and $\angle3$ form a linear - pair situation. The equation for the sum of these angles is $m\angle1 + m\angle2 + m\angle3=180^{\circ}$.

Step2: Determine the measure of $\angle1$

From the figure, $\angle1$ is a right - angle, so $m\angle1 = 90^{\circ}$.

Step3: Solve for $m\angle2 + m\angle3$

Substitute $m\angle1 = 90^{\circ}$ into the equation $m\angle1 + m\angle2 + m\angle3 = 180^{\circ}$. We get $90^{\circ}+m\angle2 + m\angle3 = 180^{\circ}$. Then, by subtracting 90 degrees from both sides of the equation, $m\angle2 + m\angle3=180^{\circ}-90^{\circ}=90^{\circ}$.

Answer:

C. 90; $m\angle1 + m\angle2 + m\angle3 = 180$. $m\angle1 = 90$, so $m\angle2 + m\angle3 = 90$.