Question

If the ratio of the complimentary angle to the supplementary angle is 7 :22
Find the angle
Please anyone solve it

Answer 1

ANSWER:

Given:

• Ratio of the complimentary angle to the supplementary angle is 7 : 22.

To Find:

• The angle

Solution:

Let the angle be x.

We know that,

⇒Compliment of an angle = (90 - Angle)°

So,

⇒Compliment of angle x = 90 - x --------(1)

Also,

⇒Supplement of an angle = (180 - Angle)°

So,

⇒Supplement of angle x = 180 - x --------(2)

We are given that,

⇒Ratio of the complimentary angle to the supplementary angle = 7 : 22

That is,

⇒Complimentary angle/Supplementary angle = 7/22

From (1) & (2),

⇒(90 - x)/(180 - x) = 7/22

On cross-multiplying,

⇒22(90 - x) = 7(180 - x)

⇒1980 - 22x = 1260 - 7x

⇒1980 - 1260 = 22x - 7x

⇒15x = 720

⇒x = 720/15

⇒x = 48°

Therefore, the angle is 48°.

Formulae Used:

• Compliment of an angle = (90 - Angle)°
• Supplement of an angle = (180 - Angle)°

Verification:

We are given that,

⇒Complimentary angle/Supplementary angle = 7/22

⇒(90 - x)/(180 - x) = 7/22

Putting x = 48°,

⇒(90 - 48)/(180 - 48) = 7/22

⇒42/132 = 7/22

⇒7/22 = 7/22

As, LHS = RHS,

HENCE VERIFIED!!!