Find the measure of an angle whose supplement is sixteen times its complement. Hint: Supplement and complement of an angle are (180-0) and (90-0) respectively.

Question

Mathematics

Ho

22 July, 20:10

Find the measure of an angle whose supplement is sixteen times its complement. Hint: Supplement and complement of an angle are (180-0) and (90-0) respectively.

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Answers (2)

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Jeffery · Answer 1

The angle is 84 degrees

Step-by-step explanation:

Let's call the angle by 'x'.

the supplement of x is equal to 180-x, and the complement of x is equal to 90-x.

If the supplement is sixteen times the complement, we can write the following equation:

(180 - x) = 16 * (90 - x)

180 - x = 1440 - 16x

16x - x = 1440 - 180

15x = 1260

x = 84

The angle is 84 degrees.

Rodrigo Smith · Answer 2

84⁰

Step-by-step explanation:

Complement = 90 - x

Supplement = 180 - x

Given:

180 - x = 16 (90 - x)

180 - x = 1440 - 16x

15x = 1260

x = 84