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: Analyze perpendicular lines

If \(\overleftrightarrow{WX}\) is perpendicular to \(\overleftrightarrow{YZ}\), then the angles formed at their intersection (point \(V\)) are right angles (\(90^\circ\)). So, \(\angle WVY\) and \(\angle XVY\) are both \(90^\circ\) (since they are adjacent angles forming a linear pair and the lines are perpendicular, each should be \(90^\circ\)).

Step2: Solve for \(a\)

We know \(m\angle WVY=(4a + 58)^\circ=90^\circ\).
Set up the equation:
\(4a+58 = 90\)
Subtract 58 from both sides:
\(4a=90 - 58\)
\(4a = 32\)
Divide both sides by 4:
\(a=\frac{32}{4}=8\)

Step3: Solve for \(b\)

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

Answer:

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