Question

The measure of ∠P is five less than four times the measure of ∠Q. If ∠P and ∠Q are supplementary angles, find m∠P

Answer 1

Answer:

P=143

Step-by-step explanation:

So, we know that P and Q are supplementary angles. In other words:

$\angle P +\angle Q =180$

We also know that P is 5 less than 4 times Q. Thus:

$\angle P=4\angle Q-5$

Substitute the second equation into the first:

$(4\angle Q-5)+\angle Q=180$

Find Q. Combine like terms:

$5\angle Q-5=180$

Add 5 to both sides:

$5\angle Q=185$

Divide both sides by 5:

$\angle Q=37$

So, Q is 37 degrees.

Q and P are supplementary, which means that P is 180-37 or 143 degrees.

And we're done!