Question

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Please tell answer with Step-by-step explanation


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 its supplementary angle? ​

Answer 1

Let the angle be x. Then its supplementary angle is 180 - x and the complementary angle is 90 - x.

Given (180 - x)/ (90 - x) = 8/3. Solving we get x = 36.

Ratio of the angle to its supplementary is 36/(180 -36) = 36/144 = 1/4.

Ans -- 1:4

Answer 2

Let the angle be x

∴ Its Supplementary angle = 180 - x (Sum of supplementary angles is 180°)

And its Complimentary angle = 90 - x (Sum of supplementary angles is 90°)

According to question

Supplementary : Complimentary = 8 : 3

( 180 - x ) : ( 90 - x ) = 8 : 3

3( 180 - x) = 8 ( 90 - x )

540 - 3x = 720 - 8x

5x = 180

x = 36

∴ Angle is 36°

Now, its supplementary angle = 180 - 36 = 144

Ratio of the angle and its supplementary angle

= 36/144 = 1/4 or 1 : 4