Question

In the diagram, ∠4 ≅ ∠5 and SE — bisects
∠RSF. Find m∠1. Explain your reasoning.

Answer 1

60°

Explanation:

You want the measure of angle 1 in the given diagram.

Angle relations

Transversal TR creates corresponding angles 1 and 5, so those are congruent.

It is given that angles 4 and 5 are congruent.

Transversal SE creates alternate interior angles 2 and 4, so those are congruent.

Angle bisector SE creates angles 2 and 3 congruent.

Now we have ∠1≅∠5≅∠4≅∠2≅∠3.

Hence all of the angles are congruent to each other, and angle 1 is 1/3 of 180°.

m∠1 = 60°