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→.

Explanation:

Step1: Recall perpendicular - angle property

When two lines are perpendicular, the angles formed are right - angles, i.e., \(90^{\circ}\).

Step2: Solve for \(a\)

Set \(m\angle W VY=90^{\circ}\). So, \(4a + 58=90\).
Subtract 58 from both sides: \(4a=90 - 58\).
\(4a=32\).
Divide both sides by 4: \(a=\frac{32}{4}=8\).

Step3: Solve for \(b\)

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

Answer:

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