Question

Use the diagram to find the measure of the given angle.

Given angle: PRQ

Answer 1

Angle QRP = 85

Explanation:

Hopefully you can see QRS and TRP both equal 180 degrees, we will use this.

QRS is the same as QRP and PRS added together. Just like TRP is TRQ and QRP. We will call QRP R for simplicities sake, and we are given a formula for PRS and TRQ. PRS = 3x+35 and TRQ = 4x+15.

So now we have two equations.

180 = QRP + PRS = R + 3x + 35

180 = TRQ + QRP = 4x + 15 + R

So it's basically a system of equations.

180 = 35 + R + 3x

145 = R + 3x

R = 145 - 3x

180 = 4x + 15 + R

Replace R with what we found in the last equation

180 = 4x + 15 + 145 - 3x

180 = x +160

x = 20

Now go back to the first equation and plug 20 in for x

R = 145 - 3x

R = 145 -3(20)

R = 145 - 60

R = 85

So Angle QRP = 85

Let em know if something doesn't make sense.

Answer 2

∠PRQ = 85°

Explanation:

∠PRS and ∠TRQ are vertical angles and congruent, thus

4x + 15 = 3x + 35 ( subtract 3x from both sides )

x + 15 = 35 ( subtract 15 from both sides )

x = 20

Hence ∠PRS = (3 × 20) + 35 = 60 + 35 = 95°

∠PRQ and ∠PRS form a straight angle and are supplementary, hence

∠PRQ = 180° - 95° = 85°