Chapter 6.2, Problem 2STP

Solve each exercise and enter your answer on the grid provided.

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 $X$?

To determine

To find: The measure of angle x .

Answer to Problem 2STP

The measure of angle X is 50.

Explanation of Solution

Given information: The sum of measures of angle x and angle y is 90. And the measure of angle x is 30 less than twice the measure of angle y .

Calculation:

For the given information set up two equations and solve them using substitution method.

The sum of measures of angle x and y is 90.

  $x+y=90$ ------(1)

The measure of angle x is 30 less than twice the measure of angle y .

  $x=2y-30$ -------(2)

Substitute x as $2y-30$ into equation (1)

  $2y-30+y=90$

Combine like terms

  $3y-30=90$

Add both sides 30.

Divide both sides by 3.

  $y=40$

Substitute y as 40 into $x=2y-30$

  $x=2(40)-30$

  $x=80-30$

  $x=50$

Hence the measure of angle X is 50.