Question

An angle is one fourth of its supplement and two fifth of its complement the measure of the angle is

Answer 1

Supplementary angles = 144 ° and 36 ° and complementary angles = 64.28 ° and 25.72 °.

Step-by-step explanation:

Let  supplementary angles = x and $\dfrac{x}{4}$

∴ $x +\dfrac{x}{4}$ = 180°

⇒ $\dfrac{5x}{4}$= 180°

⇒ x = 144 °

and $\dfrac{x}{4}$ = 36 °

Let  complementary angles = x and$\dfrac{2x}{5}$

∴ $x +\dfrac{2x}{5}$= 90°

⇒ $\dfrac{7x}{5}$= 90°

⇒ x = 64.28 °

and $\dfrac{2x}{5}$= 25.72 °

Hence, supplementary angles = 144 ° and 36 ° and complementary angles =  64.28 ° and 25.72 °.

Answer 2

Given:

An angle is one-fourth of its complement and two-fifth of its supplement.

To Find:

The measure of the angle is?

Solution:

1. It is given that an angle is 1/4th of its complement and 2/5th of its supplement.

2. Two angles are said to be the complement of each other if the sum of the angles is 180 degrees.

=> Since the angle is one-fourth of its supplement, the angles will be x and x/4

=> x +x/4 = 180,

=> 5x/4 = 180,

=> x = 144°,

=> x/4 = 36°.

Therefore, the value of the unknown angle, in this case, is 36°.

3. Two angles are said to be a supplement of each other if the sum of the angles is 90 degrees.

=> Since the angle is two-fifth of its complement, the angles will be y and 2y/5

=> y + 2y/5 = 90,

=> 7y/5 = 90,

=> 7y = 450,

=> y = 64.286°.

=> 2y/5 = 25.71°

Therefore, the value of the unknown angle, in this case, is 25.71°.

Therefore, the measure of the angles in the case of the supplement and the complement is 36°, 25.71°.