Answer:
m∠P=140°
Step-by-step explanation:
Given:
∠P and ∠Q are supplementary angles.
The measure of angle P is five less than four times the measure of angle Q.
To find m∠P
Solution:
The measure of angle P can be given as:
A) [tex]m\angle P=4(m\angle Q-5)[/tex]
And
B) [tex]m\angle P+ m\angle Q=180[/tex] [Definition of supplementary angles]
Substituting equation A into B.
[tex]4(m\angle Q-5)+ m\angle Q=180[/tex]
Solving for [tex]m\angle Q[/tex]
Using distribution:
[tex]4m\angle Q-20+ m\angle Q=180[/tex]
Simplifying by combining like terms.
[tex]5m\angle Q-20=180[/tex]
Adding 20 to both sides.
[tex]5m\angle Q-20+20=180+20[/tex]
[tex]5m\angle Q=200[/tex]
Dividing both sides by 5.
[tex]\frac{5m\angle Q}{5}=\frac{200}{5}[/tex]
[tex]m\angle Q=40[/tex]
Substituting [tex]m\angle Q=40[/tex] in equation B.
[tex]m\angle P+ 40=180[/tex]
Subtracting both sides by 40.
[tex]m\angle P+ 40-40=180-40[/tex]
[tex]m\angle P=140[/tex]
Thus, we have:
m∠P=140° (Answer)