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

Let the measure of angle Y be y.
The measure of angle X is 2y - 30, because it is 30 less than twice the measure of angle Y.
The sum of the measures of angle X and angle Y is 90, so y + (2y - 30) = 90.
Combining like terms, we get 3y - 30 = 90.
Adding 30 to both sides, we get 3y = 120.
Dividing both sides by 3, we get y = 40.
Substituting this value back into the equation 2y - 30, we get 2(40) - 30 = 80 - 30 = 50.
The measure of angle X is 50 degrees. Answer: \boxed{50}.