find the measure of an angle if the sum of the measures of its complement and supplement is 162 degrees.
Let X = the angle.
90 - X = the complementary angle.
180 - X = the supplementary angle.
We add those together to get the sum equal to 162 degrees.
(90 - X) + (180 - X) = 162
and solve for X.
An angle measures 162° more than the measure of its supplementary angle. What is the measure of each angle?
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To find the measure of the angle, let's denote the angle as "x".
The complement of the angle is 90 - x degrees, and the supplement of the angle is 180 - x degrees.
According to the given condition, the sum of the measures of the complement and supplement is 162 degrees:
(90 - x) + (180 - x) = 162
To solve this equation, let's simplify:
90 - x + 180 - x = 162
270 - 2x = 162
Next, let's isolate the variable term:
-2x = 162 - 270
-2x = -108
To solve for x, divide both sides by -2:
x = -108 / -2
x = 54
Therefore, the measure of the angle is 54 degrees.
To verify this, let's check the complement and supplement:
Complement: 90 - 54 = 36 degrees
Supplement: 180 - 54 = 126 degrees
And indeed, the sum of the complement (36) and the supplement (126) is 162 degrees.