Question

Hi
ratio of measures of supplementary angle to complementary angle of an angle is 8:3
what is the ratio of the angle to its supplementary angle?


Please tell me answer of this question in easy way but Step-by-step explanation


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Answer 1

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The ratio of the measures of the supplementary angle to the complementary angle of a given angle is 8:3. What will be the ratio of the angle to it's supplementary?

Let the measure of the given angle be x. Complementary angle for x would be 90 - x and supplementary angle would be 180 - x. Thus 180 - x / 90 - x = 8 / 3.

Hence 3 (180 - x) = 8 (90 - x), and 540 - 3 x = 720 - 8 x.

Thus 5 x = 180 and x = 36.

This means that the measure of the given angle is 36 degrees.

Hence supplementary angle of 36 degrees is 144 degrees.

Thus ratio of the angle to its supplementary angle is 1 : 4.

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