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? (1 point) Responses 20° 20° 35° 35° 50° 50° 65°
Answers
GPT 3.5
Let's say the measure of angle Y is represented by y.
Since the sum of the measures of angle X and angle Y is 90, we can write the equation: X + Y = 90.
We are also told that the measure of angle X is 30 less than twice the measure of angle Y. In equation form, this is: X = 2Y - 30.
Substituting the second equation into the first equation, we get: (2Y - 30) + Y = 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.
Therefore, the measure of angle X is 2(40) - 30 = 80 - 30 = 50 degrees.
So the answer is 50°.
Since the sum of the measures of angle X and angle Y is 90, we can write the equation: X + Y = 90.
We are also told that the measure of angle X is 30 less than twice the measure of angle Y. In equation form, this is: X = 2Y - 30.
Substituting the second equation into the first equation, we get: (2Y - 30) + Y = 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.
Therefore, the measure of angle X is 2(40) - 30 = 80 - 30 = 50 degrees.
So the answer is 50°.