Question

if the ( mangle srw = 85^{circ} ), what are the measures of ( angle vru ) and ( angle urw )?
( mangle vru = 85^{circ} )
( mangle urw = )
5
10
15
20

Explanation:

Step1: Find the value of \(x\)

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

Step2: Calculate \(\angle URW\)

\(\angle URW=(2x + 15)-(2x + 10)\)
Expand: \(2x+15 - 2x - 10\)
Simplify: \(5^{\circ}\)

Answer:

\(m\angle VRU = 85^{\circ}\), \(m\angle URW = 5^{\circ}\)