Final answer:
To find the measure of angle X, we use the given relationships involving angles A, Y, and X. After setting up equations and solving for angle Y, we find that Y is 40 degrees, which makes angle X equal to 50 degrees.
Step-by-step explanation:
The question asks us to find the measure of angle X given that the sum of the measures of angle A and angle Y is 90 degrees and that the measure of angle X is 30 degrees less than twice the measure of angle Y. We denote the measure of angle Y as 'y'.
Since the sum of angles A and Y is 90 degrees, we can write this relationship as:
A + Y = 90 degrees
Angle X, as given, is 30 degrees less than twice angle Y:
X = 2Y - 30 degrees
However, angle A is not given, nor is it necessary to find it for solving the problem, so we only need to focus on angles X and Y. We can solve for Y by realizing that the three angles must add up to 180 degrees if they are part of the same triangle or a set of supplementary angles:
A + Y + X = 180 degrees
Substitute the expression for X:
A + Y + (2Y - 30) = 180 degrees
Combine terms with Y:
A + 3Y - 30 = 180 degrees
Since A and Y add up to 90 degrees:
90 + 3Y - 30 = 180 degrees
Simplify and solve for Y:
3Y + 60 = 180 degrees
3Y = 120 degrees
Y = 40 degrees
Now, plug the value of Y back into the equation for X:
X = 2(40) - 30
X = 80 - 30
X = 50 degrees
Therefore, the measure of angle X is 50 degrees, which corresponds to option C.