Question

if the complement of an angle is 2 less than one fifth of it's supplement then the measure of it's complement is​

Answer 1

Answer:

Two angles which are complementary add up to 90

o

.

as per problem given,

x+

5

1

x=90

⇒

5

6

x=90

x=90×

6

5

=75

Thus one angle is 75

o

other will be

5

75

=15

o

angle which is one fifth of its complement is 15 degree.

Answer 2

Given: The complement of an angle is 2° less than one fifth of its supplement.

To find: Measure of its complement

Explanation: The complement of an angle is the measure of the angle which when added to actual angle results in 90°.

Let the angle be x.

Its complement= 90-x

The supplement of an angle is the measure of the angle which when added to actual angle results in 180°.

Let the angle be x.

Its supplement= 180-x

1/5 of its supplement= 180-x / 5

According to question, the complement of angle is 2° less than 1/5 of its supplement.

Then,

=>$90 - x = \frac{180 - x}{5} - 2$

=>$90 - x = \frac{180 - x - 10}{5}$

=>5 (90-x) = 170-x

=> 450 - 5x = 170-x

=> 4x = 280

=> x = 280/4

= 70°

Therefore, the angle is 70°.

Its complement= 90°-x

= 90°-70°

= 20°

Therefore, the measure of the complement of the angle is 20°.