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…
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→.
Answer
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)