Question

if $m\angle4 = 35$, find $m\angle3$. explain.
a. 55; $\angle3$ and $\angle4$ are complementary angles, so $m\angle3 = 90 - m\angle4$.
b. 35; $\angle3$ and $\angle4$ are corresponding angles, so $m\angle3 = m\angle4$.
c. 145; $\angle3$ and $\angle4$ are supplementary angles, so $m\angle3 = 180 - m\angle4$.
d. 35; $\angle3$ and $\angle4$ are alternate interior angles, so $m\angle3 = m\angle4$.

Explanation:

Step1: Identify angle relationship

We know $\angle 1$ and $\angle 3$ are right angles ($90^\circ$), so lines $AB$ and $CD$ are parallel. $BC$ is a transversal. $\angle 3$ and $\angle 4$ add up to $90^\circ$, meaning they are complementary.

Step2: Calculate $m\angle 3$

Use complementary angle rule: $m\angle 3 = 90^\circ - m\angle 4$
Substitute $m\angle 4=35^\circ$: $m\angle 3 = 90 - 35 = 55^\circ$

Answer:

A. 55; $\angle 3$ and $\angle 4$ are complementary angles, so $m\angle 3 = 90 - m\angle 4$.