Find the measure of angle RPF

124°

Step-by-step explanation: Notice that angles CPF and RPB are vertical <'s.

Vertical angles are two angles that share a common

endpoint and whose sides form opposite rays.

Since these angles have the same measure,

we can setup the equation 4t + 88 = 2t + 72.

Now subtract 2t from both sides and we have 2t + 88 = 72.

Now subtract 88 from both sides to get 2t = -16.

Solving from here, we find that t = -8.

Now notice that <FPB is a straight angle which

means that it measures exactly 180 degrees.

So let's substitute a 4 into the measure of angle CPF.

So we have 4(-8) + 88 or -32 + 88 which is 56°.

Since FPC and CPB are a linear pair, we know that are supplementary.

If two angles are supplementary, then the sum of their measures is 180 degrees which means we take 180 minus the measure of <CPF.

So we have 180 - 56 which is 124°.

Now since <CPB and <FPR are vertical angles

So<FPR must also measure 124°