Question

In the above figure, m∠P = 105° and m∠Q = 5x. If angles P and Q are supplementary angles, what is the value of x and the measure of angle Q? A. x = 15, m∠Q = 20° B. x = 15, m∠Q = 75° C. x = 57, m∠Q = 75° D. x = 39, m∠Q = 195°

Answer 1

B. x = 15, m∠Q = 75°

Explanation:

Given:

m∠P = 105°

m∠Q =
`5x`

Angles P and Q are supplementary angles

To find value of
`x` and m∠Q.

Solution:

`m\angle P+m\angle Q =180\°` [Sum of supplementary angles =180°]

`105+5x =180` [Substitution ∵ m∠P = 105° and m∠Q =
`5x` ]

Subtracting both sides by 105°.

`105+5x-105 =180-105`

`5x =75`

Dividing both sides by 5.

`(5x)/(5) =(75)/(5)`

∴
`x=15`

∴
`m\angle Q=5x=5* 15=75\°`