Answer:
70 degrees.
Step-by-step explanation:
Let the angle be x then:
Its supplement is 180-x.
Its complement = 90 - x.
The supplement of the complement = (180 - (90 - x) = 90 + x.
So we have the equation:
180 - x = 2(90 + x) - 60.
180 - x = 180 + 2x - 60
- x - 2x = 180 - 180 - 60
-3x = -60
x = 20 degrees
So the measure of the complement = 90 - 20 = 70 degrees.
Two angles are supplementary if their measures add up to 180°, while two angles are complementary if their measures add up to 90°.
Knowing this, we will find that the measure of the complement is 70°
Let's see how to get that.
Let's define A as our angle.
We know that:
"The supplement of an angle is 60 degrees less than twice the supplement of the complement of the angle"
The supplement of this angle is B such that:
A + B = 180°
B = 180° - A.
The complement of the angle is C, such that:
A + C = 90°
C = 90° - A
The supplement of the complement (the supplement of C) is D:
D + C = 180°
D + (90° - A) = 180°
D = 90° + A
Then we can write the expression:
180° - A = 2*(90° + A) - 60°
Now we can solve this for A.
180° - A = 180° + 2*A - 60°
60° = 2*A + A + 180° - 180°
60° = 3*A
60°/3 = A = 20°
The original angle's measure is 20°.
Then the complement is:
C = 90° - A = 90° - 20° = 70°
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