Question

∠p and ∠q are supplementary and ∠r and ∠p are supplementary. complete the proof that ∠r≅∠q.
statement reason
1 ∠p and ∠q are supplementary given
2 ∠r and ∠p are supplementary given
3 m∠p + m∠q = 180° definition of supplementary angles
4 m∠r + m∠p = 180° definition of supplementary angles
5 m∠p + m∠q = m∠r + m∠p transitive property of equality
6 m∠r = m∠q properties of addition, subtraction, multiplication, and division
7

Explanation:

Step1: Recall angle - congruence definition

If two angles have the same measure, they are congruent.

Step2: Analyze step 6 result

We have $m\angle R=m\angle Q$ from step 6.

Step3: Write the final statement

$\angle R\cong\angle Q$ by the definition of congruent angles (angles with equal measures are congruent).

Answer:

1. $\angle R\cong\angle Q$; Definition of congruent angles