Question

no iready minutes this week

1. set - up and solve an equation to find the value of x.

x =
m∠xwu

Explanation:

Step1: Find the third angle in triangle VUW

The sum of angles in a triangle is \(180^\circ\). So, the angle at \(W\) inside the triangle (\(\angle VWU\)) is \(180^\circ - 98^\circ - 31^\circ\).
\[180 - 98 - 31 = 51^\circ\]

Step2: Use linear pair property

\(\angle VWU\) and \(\angle XWU\) are a linear pair, so they add up to \(180^\circ\). Also, \(\angle XWU=(7x - 32)^\circ\) and \(\angle VWU = 51^\circ\), so:
\[51+(7x - 32)=180\]
Simplify the left side:
\[7x + 19 = 180\]
Subtract 19 from both sides:
\[7x = 180 - 19\]
\[7x = 161\]
Divide both sides by 7:
\[x=\frac{161}{7}=23\]

Step3: Find \(m\angle XWU\)

Substitute \(x = 23\) into \((7x - 32)^\circ\):
\[7(23)-32=161 - 32 = 129^\circ\]

Answer:

\(x = 23\), \(m\angle XWU = 129^\circ\)