Question

wx and yz intersect at point v. if m∠wvy = (4a + 58)° and m∠xvy = (2b − 18)°, find the values of a and b such that wx is perpendicular to yz.
a=
b=

Explanation:

Step1: Recall perpendicular lines form right angles.

If \(\overleftrightarrow{WX}\) is perpendicular to \(\overleftrightarrow{YZ}\), then the angles formed at their intersection (point \(V\)) are right angles (\(90^\circ\)). So, \(m\angle WVY = 90^\circ\) and \(m\angle XVY = 90^\circ\).

Step2: Solve for \(a\) using \(m\angle WVY = 90^\circ\).

We have \(m\angle WVY=(4a + 58)^\circ\). Set this equal to \(90^\circ\):
\[
4a+58 = 90
\]
Subtract 58 from both sides:
\[
4a=90 - 58
\]
\[
4a = 32
\]
Divide both sides by 4:
\[
a=\frac{32}{4}=8
\]

Step3: Solve for \(b\) using \(m\angle XVY = 90^\circ\).

We have \(m\angle XVY=(2b - 18)^\circ\). Set this equal to \(90^\circ\):
\[
2b-18 = 90
\]
Add 18 to both sides:
\[
2b=90 + 18
\]
\[
2b = 108
\]
Divide both sides by 2:
\[
b=\frac{108}{2}=54
\]

Answer:

\(a = 8\), \(b = 54\)