Question

$$\overleftrightarrow{wx}$$ and $$\overleftrightarrow{yz}$$ intersect at point v. if $$m\angle w v y = ( 4 a + 5 8 ) ^ { \circ }$$ and $$m\angle x v y = ( 2 b - 1 8 ) ^ { \circ }$$, find the values of a and b such that $$\overleftrightarrow{wx}$$ is perpendicular to $$\overleftrightarrow{yz}$$.

Explanation:

Step1: Use the property of perpendicular lines

If \(\overleftrightarrow{WX}\perp\overleftrightarrow{YZ}\), then \(m\angle WVY = 90^{\circ}\) and \(m\angle XVY=90^{\circ}\).
For \(m\angle WVY=(4a + 58)^{\circ}\), set up the equation \(4a+58 = 90\).
Subtract 58 from both sides: \(4a=90 - 58\), so \(4a = 32\).
Divide both sides by 4: \(a=\frac{32}{4}=8\).

Step2: Solve for \(b\)

For \(m\angle XVY=(2b-18)^{\circ}\), set up the equation \(2b - 18=90\).
Add 18 to both sides: \(2b=90 + 18\), so \(2b=108\).
Divide both sides by 2: \(b=\frac{108}{2}=54\).

Answer:

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