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An angle measures 4 times its complement. What is the supplement of the smaller angle?

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27spidersmart

Answer:

Supplement of smaller angle is 120°.

Step-by-step explanation:

We write 'angle' as the variable x.

A supplementary angle totals of 180° and a complementary angle totals of 90°.

We get an equation by - x on both sides because it says the sum is equal to 180°/90°.

180° - x is for the supplementary angle.

90° - x is for the complementary angle.

Since it says 4 times the complement, we multiply the complementary angle with 4 and make it into an equation-

180° - x = 4 × (90° - x)

180° - x = 360° - 4x

3x = 180°

x = 60°

We insert the x into the two 180° - x and 90° - x -

Supplementary angle: 180° - 60° = 120°

Extra:

Complementary angle: 90° - 60° = 30°

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