Help with Geometry work

Question

in triangle QPL if m<Q is five times m<p and m<L is twelve more than twice m<p. find the measure of <P

Answer 1

Start with the information we're given or what we know:

Q = 5P (The measure of angle Q is five times the measure of angle P)

L = 2P + 12 (The measure of angle L is twelve more than twice the measure of angle P)

Q + P + L = 180 (We know that the angles of a triangle add up to 180°)

Let's substitute what we know to get P as the only variable in order to solve for it:

Q + P + L = 180

(5P) + (P) + (2P + 12)

5P + P + 2P + 12 = 180

8P + 12 = 180 (Combine like terms and solve for P)

-12 -12

8P = 168

8 8

P = 21

We can check our answer:

If Q is five times P then Q = 5P = 5(21) = 105

If L is 12 more than twice P then L = 2P + 12 = 2(21) + 12 = 42 + 12 = 54

105 + 54 + 21 should equal 180 and it does so our answer is correct

The measure of angle P is 21°

Answer 2

Let m∠P = x

Then m∠Q = 5x

And m∠L = 12 + 2x

We know that the sum of all the angles is 180° so:

x + 5x + 12 + 2x = 180

8x + 12 = 180

8x = 168

x = 21

So m∠P is 21°