Question

statement reason 1 ∠sru and ∠ruv are supplementary given 2 m∠sru + m∠ruv = 180° definition of supplementary angles 3 m∠prs + m∠sru = 180° angles forming a linear pair sum to 180° 4 m∠sru + m∠ruv = m∠prs + m∠sru transitive property of equality 5 6

Explanation:

Step1: Start from step 4

We have $m\angle SRU + m\angle RUV=m\angle PRS + m\angle SRU$.

Step2: Subtract $m\angle SRU$ from both sides

By the subtraction - property of equality, if $a + b=a + c$, then $b = c$. So, $m\angle RUV=m\angle PRS$.

Answer:

$m\angle RUV=m\angle PRS$