Question

Two angles are supplementary. If angle A is five times the sum of the angle B plus 7. 2, what is angle B

Answer 1

Angle B = 24°

Explanation:

Given:

• Angles are supplementary
• Angle A is 5 times the sum of angle B plus 7.2

that means, Angle A = 5 ( Angle B + 7.2 )

Now,

Let Angle B = x (say)

•.• Angle A = 5 ( x + 7.2 )

• Supplementary angles are a pair of angles that make sum of 180° .

Therefore, As it is given that the angles are supplementary , the sum of Angle A and Angle B will be equal to 180°.

Angle A + Angle B = 180°

`⇢x + 5(x + 7.2) = 180`

`⇢x + 5x + 36 = 180`

`⇢6x = 180 - 36`

`⇢6x = 144`

`⇢x = (144)/(6)`

`⇢ \boxed{x = 24}`

Now, substituting the value of x. . .

• Angle B = 24°
• Angle A = 5( 24+ 7.2 ) = 5( 31.2 ) = 156°

Thus, Angle B comes out 24°