Question

the ratio of the measures of the supplementsupplementary angle to complementary of a given angle. is 8:3 . what will be the ratio of the angle to its supplementary angle

Answer 1

Answer:

Step-by-step explanation:

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.

Answer 2

Let the angle be x

Its supplementary angle = 180 - x

Its complementary angke = 90 - x


According to the given condition,

180 - x / 90 - x = 8 / 3

Cross multiply

∴ 3(180 - x) = 8(90 - x)

∴ 540 - 3x = 720 - 8x

∴ 5x = 720 - 540

∴ 5x = 180

Divide both the sides by 5

∴ x = 36


∴ The measure of the angle is 36°


∴ Supllementary angle ➾ 180 - x

➾ 180 - 36

➾ 144°


∴ Ratio of the angle to its supplementary angle ➾ 36 / 144

Divide by 36

➾ 1 / 4

∴ Ratio = $\boxed{\boxed{\textsf{1 : 4}}}$