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twice the supplement of an angle is 34 degrees more than 4 times its complement. what is the angle?

Sagot :

Angle:  x
Angle's supplement:  180 - x    (Two supplementary angles have a sum of 180°)
Angle's complement:  90 - x     (Two complementary angles have a sum of 90°)

Equation:

2(180 - x) = 4 (90 - x) + 34
360 - 2x = 360 - 4x + 34
4x - 2x = 360 + 34 - 360
2x = 34
2x/2 = 34/2
x = 17   The angle's measure is 17 degrees.

Supplement of the angle: 180 - x ⇒ 180 - 17 = 163 degrees
Complement of the angle:  90 - x ⇒ 90 - 17 = 73 degrees

To check: 
2 (180-x) = 4 (90-x) + 34
2 (180-17) = 4 (90-17) + 34
2 (163) = 4 (73) + 34
326 = 292 + 34
326 = 326