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

Answer:

B. x = 15, m∠Q = 75°

Step-by-step 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.

$\frac{5x}{5} =\frac{75}{5}$

∴ $x=15$

∴ $m\angle Q=5x=5\times 15=75\°$