Answer:
P=143
Step-by-step explanation:
So, we know that P and Q are supplementary angles. In other words:
[tex]\angle P +\angle Q =180[/tex]
We also know that P is 5 less than 4 times Q. Thus:
[tex]\angle P=4\angle Q-5[/tex]
Substitute the second equation into the first:
[tex](4\angle Q-5)+\angle Q=180[/tex]
Find Q. Combine like terms:
[tex]5\angle Q-5=180[/tex]
Add 5 to both sides:
[tex]5\angle Q=185[/tex]
Divide both sides by 5:
[tex]\angle Q=37[/tex]
So, Q is 37 degrees.
Q and P are supplementary, which means that P is 180-37 or 143 degrees.
And we're done!
