Question

1. in the figure, eh || bi and bi || cj.

a. what is m∠1? explain.
b. what is m∠3? explain.

1. definition of congruence

Explanation:

Step1: Identify angle - relationship for ∠1

∠1 and the 53 - degree angle are vertical angles.
Vertical angles are congruent.

Step2: Determine m∠1

Since vertical angles are equal, m∠1 = 53°.

Step3: Identify angle - relationship for ∠3

EH || BI and BI || CJ, so EH || CJ.
∠3 and the 53 - degree angle are corresponding angles.
Corresponding angles formed by parallel lines are congruent.

Step4: Determine m∠3

Since corresponding angles are equal, m∠3 = 53°.

Answer:

a. m∠1 = 53° because vertical angles are congruent.
b. m∠3 = 53° because corresponding angles formed by parallel lines are congruent.