Question

if the ( mangle srw = 85^{circ} ), what are the measures of ( angle vru ) and ( angle urw )?
( mangle vru=)
( mangle urw = 15^{circ} )

Explanation:

Step1: Find the value of \(x\)

Since \(\angle SRW = 85^{\circ}\), and \(\angle SRW\) and \((2x + 10)^{\circ}\) are vertical angles. So \(2x+10 = 85\).
Subtract \(10\) from both sides: \(2x=85 - 10=75\).
Divide both sides by \(2\): \(x = 37.5\).

Step2: Calculate \(m\angle VRU\)

Substitute \(x = 37.5\) into \((2x + 15)^{\circ}\).
\(2x+15=2\times37.5 + 15=75+15 = 90^{\circ}\).

Answer:

\(m\angle VRU = 90^{\circ}\)