Answer:
Find m∠P and m∠Q if ∠P and ∠Q are supplementary, m∠P=2x+15 , and m∠Q=5x−38 .
The sum of the measures of two supplementary angles is 180° .
So, m∠P+m∠Q=180°
Substitute 2x+15 for m∠P and 5x−38 for m∠Q .
2x+15+5x−38=180°
Combine the like terms. We get:
7x−23=180°
Add 23 to both the sides. We get:
7x=203°
Divide both the sides by 7 .
7x7=203°7
Simplify.
x=29°
To find m∠P , substitute 29 for x in 2x+15 .
2(29)+15=58+15
Simplify.
58+15=73
So, m∠P=73° .
To find m∠Q , substitute 29 for x in 5x−38 .
5(29)−38=145−38
Simplify.
145−38=107
So, m∠Q=107° .
