In a figure, one complementary angle has a measure of 36° and the other has a measure of (x−3)° . What is the value of x and the value of the unknown angle measure?
Two angles are complementary if their sum equals 90 degrees. In this case, we have one angle measuring 36 degrees, and the other angle measuring (x-3) degrees.
Therefore, we can set up the equation:
36 + (x-3) = 90
Simplifying this equation, we get:
x + 33 = 90
Subtracting 33 from both sides, we have:
x = 90 - 33
x = 57
So the value of x is 57.
To find the measure of the unknown angle, we substitute the value of x back into the expression (x-3):
(x-3) = (57-3) = 54
Therefore, the unknown angle measures 54 degrees.