Question

WZ and YZ intersect at point V. If WVY = 4a+58 and XVY = 2b-18, find the values of a and b so that WX is perpendicular to YZ

Answer 1

The values of 'a' and 'b' are  8 and 54 respectively.

Explanation

As WX and YZ are perpendicular to each other and they intersect at point V , so both ∠WVY and ∠XVY are 90°.

Given that, ∠WVY = 4a+58  and  ∠XVY = 2b-18

That means....

$4a+58=90 \\ \\ 4a= 90-58\\ \\ 4a=32 \\ \\ a= \frac{32}{4}=8$

and

$2b-18 =90 \\ \\ 2b= 90+18\\ \\ 2b= 108\\ \\ b= \frac{108}{2}= 54$

So, the values of 'a' and 'b' are  8 and 54 respectively.