Question

if $m\angle4 = 35$, find $m\angle2$. explain.

a. 55; $\angle2$ and $\angle4$ are complementary angles, so $m\angle2 = 90 - m\angle4$.
b. 35; $\angle2$ and $\angle4$ are corresponding angles, so $m\angle2 = m\angle4$.
c. 145; $\angle2$ and $\angle4$ are supplementary angles, so $m\angle2 = 180 - m\angle4$.
d. 35; $\angle2$ and $\angle4$ are alternate interior angles, so $m\angle2 = m\angle4$.

Explanation:

Step1: Identify angle relationship

$\angle 2$ and $\angle 4$ are alternate interior angles formed by transversal $BC$ cutting parallel lines $AB$ and $CD$.

Step2: Apply alternate interior angles theorem

Alternate interior angles are congruent, so $m\angle 2 = m\angle 4$.

Step3: Substitute given angle measure

Since $m\angle 4 = 35$, $m\angle 2 = 35$.

Answer:

D. 35; $\angle 2$ and $\angle 4$ are alternate interior angles, so $m\angle 2 = m\angle 4$.