Question

if the m∠srw = 85°, what are the measures of ∠vru and ∠urw? m∠vru =
m∠urw =
(2x + 15)° (2x + 10)°

Explanation:

Step1: Set up an equation using vertical - angle equality

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

Step2: Set up an equation for supplementary angles

$\angle VRU$ and $\angle URW$ are supplementary, so $m\angle VRU + m\angle URW=180^{\circ}$. Substitute $m\angle VRU = 85^{\circ}$ into the equation: $85^{\circ}+m\angle URW = 180^{\circ}$.

Step3: Solve for $m\angle URW$

$m\angle URW=180 - 85=95^{\circ}$.

Answer:

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