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?
a. 20 degrees***
b. 35 degrees
c. 50 degrees
d. 65 degrees
x + y = 90
x = 2 y - 30 (use that for x)
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(2 y - 30) + y = 90
3 y = 120
y = 40
so x = 50
well, if x=20, then y=70, since they add to 90.
does 20 = 2*70-30?
what did you do first?
so is the answer 50?
x + y = 90 -a
x = 2 y - 30 -b
these are the two equations you get from the question.
b cab written as x-2y=30
now a-b then you get x as 50
To solve this problem, we need to set up an equation based on the given information and then solve for the measure of angle X.
Let's suppose the measure of angle Y is represented by the variable 'y'. According to the problem, the measure of angle X is 30 less than twice the measure of angle Y. So, we can express the measure of angle X as 2y - 30.
The sum of the measures of angle X and angle Y is 90. Therefore, we can write the equation as:
X + Y = 90
Substituting the expressions for X and Y, we get:
(2y - 30) + y = 90
Now we can solve for 'y':
2y - 30 + y = 90
3y - 30 = 90
3y = 120
y = 40
So, the measure of angle Y is 40 degrees.
Finally, we can substitute the value of 'y' into the expression for angle X:
X = 2y - 30
X = 2(40) - 30
X = 80 - 30
X = 50
Therefore, the measure of angle X is 50 degrees.
The correct answer is (c) 50 degrees.