Question

if the m∠srw = 85°, what are the measures of ∠vru and ∠urw? m∠vru = m∠urw =

Explanation:

Step1: Note vertical - angle relationship

Vertical angles are equal. $\angle SRW$ and $\angle VRU$ are vertical angles. So $m\angle VRU=m\angle SRW$.
Since $m\angle SRW = 85^{\circ}$, then $m\angle VRU=85^{\circ}$.

Step2: Use linear - pair relationship

$\angle VRU$ and $\angle URW$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$.
Let $m\angle URW = y$. Then $m\angle VRU + y=180^{\circ}$.
Substitute $m\angle VRU = 85^{\circ}$ into the equation: $85^{\circ}+y = 180^{\circ}$.
Solve for $y$: $y=180^{\circ}-85^{\circ}=95^{\circ}$. So $m\angle URW = 95^{\circ}$.

Answer:

$m\angle VRU = 85^{\circ}$
$m\angle URW = 95^{\circ}$