Question

if m∠4 = 35, find m∠3. explain.
a. 55. ∠3 and ∠4 are complementary angles so m∠3 = 90 - m∠4
b 35 ∠3 and ∠4 are corresponding angles so m∠3 = m∠4
c 145 ∠3 and ∠4 are supplementary angles so m∠3 = 180 - m∠4
d 35 ∠3 and ∠4 are alternate interior angles so m∠3 = m∠4

Explanation:

Step1: Identify angle - relationship

$\angle3$ and $\angle4$ are complementary angles (since the angle formed by the intersection of the perpendicular line and the other line is a right - angle, and the sum of $\angle3$ and $\angle4$ is 90 degrees).

Step2: Use the complementary - angle formula

The formula for complementary angles is $m\angle3 + m\angle4=90^{\circ}$, so $m\angle3 = 90 - m\angle4$.

Step3: Substitute the value of $m\angle4$

Given $m\angle4 = 35^{\circ}$, then $m\angle3=90 - 35=55^{\circ}$.

Answer:

A. 55. $\angle3$ and $\angle4$ are complementary angles so $m\angle3 = 90 - m\angle4$