Question

the ratio between the complementary and supplementary angles of an angle is in 1:7 what is the measure of angle ?​

Answer 1

Answer:

➡️Refer to the above attachment

Answer 2

The measure of angle is 75°

Step-by-step explanation:

• Given that angle = X

• Then complementary angle of X = 90° - X

• Also supplementary angle of X = 180° - X

• It is given that the ratio between the complementary and supplementary angles of an angle is in 1:7 .

• Means

        $\mathbf{\frac{complementary \ angle}{supplementary \ angle}=\frac{1}{7}}$

        $\mathbf{\frac{90-X}{180-X}=\frac{1}{7}}$

• By cross- multiplication

        7(90 -X) = 180 -X

        630 - 7 X = 180 - X

        -7 X + X = 180 - 630

        - 6 X = -450

         6 X = 450

• So

        X = 75° = This is the measure of angle