Question

The sum of the measures of angle x and angle y is 90. If the measure of angle x is 30 less than twice the measure of angle y, what is the measure of angle x?

Answer 1

The measure of angle x is 50 degree

Solution:

Given that

Sum of the measures of angle x and angle y is 90

Also given that measure of angle x is 30 less than twice the measure of angle y

Need to determine x.

Twice of angle y = 2y

30 less than twice of angle y = 2y – 30

And as x is 30 less than twice of angle y, we get

x = 2y – 30 ------(1)

Also as sum of measure of two angles is 90 so we get ,

x + y = 90

y = 90 – x -------(2)

On substituting value of y from equation 2 , we get

x = 2(90 – x) – 30

=> x = 180 – 2x – 30

=> x + 2x = 180 – 30

=> 3x = 150

=> x = 50

Hence measure of angle is 50 degree