Question

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

Answer:

1:4

Step-by-step explanation:

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

$\frac{180-x}{90-x}=\frac{8}{3}$

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

Answer 2

Answer:

Step-by-step explanation:

et 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