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 the measure of ∠1

We can see that ∠1 is a right - angle, so $m\angle1 = 90^{\circ}$.

Step2: Use the angle - sum property of a triangle

The angles ∠1, ∠2, and ∠3 are part of a triangle. The sum of the interior angles of a triangle is $180^{\circ}$. So, $m\angle1+m\angle2 + m\angle3=180^{\circ}$.

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 $90^{\circ}$ from both sides of the equation, we find that $m\angle2 + m\angle3=180^{\circ}-90^{\circ}=90^{\circ}$.

Answer:

D. 90; ∠1 + ∠2+∠3 = 180. m∠1 = 90, so m∠2 + m∠3 = 90.