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

Observe that $\angle3$ and $\angle4$ form a right - angle. Complementary angles add up to 90 degrees.

Step2: Calculate $m\angle3$

Since $m\angle3 + m\angle4=90^{\circ}$ and $m\angle4 = 35^{\circ}$, then $m\angle3=90 - m\angle4$.
Substitute $m\angle4 = 35$ into the formula: $m\angle3=90 - 35=55^{\circ}$.

Answer:

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