Question

what is $m\angle2 + m\angle3$? explain.

a. 180; $m\angle1 + 90 = 180$, so $m\angle2 + m\angle3 = 180$.
b. 180; $m\angle1 + 90 = m\angle2 + m\angle3$, so $m\angle2 + m\angle3 = 180$.
c. 90; $m\angle1 + m\angle2 + m\angle3 = 180$, $m\angle1 = 90$, so $m\angle2 + m\angle3 = 90$.
d. 90; $\angle2$ and $\angle3$ are corresponding angles, so $m\angle2 + m\angle3 = 90$.

Explanation:

First, note that lines AB and CD are parallel, and AC is perpendicular to both, so $m\angle 1 = 90^\circ$. The sum of angles in triangle ABC is $180^\circ$, meaning $m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ$. Substitute $m\angle 1 = 90^\circ$ into this equation to solve for $m\angle 2 + m\angle 3$. Option C correctly uses this angle sum property, while other options have incorrect reasoning (A/B use wrong angle relationships, D misidentifies angle types).

Answer:

C. 90; $m\angle 1 + m\angle 2 + m\angle 3 = 180$, $m\angle 1 = 90$, so $m\angle 2 + m\angle 3 = 90$.