Question

Would someone please help me out with Geometry?? I tried yesterday with other questions and got no help.

Thank you so much!!

Answer 1

Problem 16.

Angles NPR and PTS are congruent bec they are corresponding angles.
3x = 5x - 32
-2x = -32
x = 16

m<PTS = 5x - 32 = 5(16) - 32 = 80 - 32 = 48

Angles PTS and PTU form a linear pair and are supplementary.

m<PTS + m<PTU = 180

48 + m<PTU = 180

m<PTU = 132

Problem 17.

Look at the angle in the right upper side of 89 deg.
Angle QTU also measures 89 deg since it is a corresponding angle tot eh 89-deg angle above.

Angle QTU and QTS are a linear pair and are supplementary, so angle QTS measures 91 deg.

We know from problem 16 that angle PTS measures 48 deg.

m<QTP = m<QTS - m<PTS = 91 - 48 = 43

Answer 2

First, you need to find ∠PTS because ∠PTS is complementary to ∠PTU and once you find the measurement, you just have to subtract it from 180. 

∠PTS is a corresponding angle to ∠NPR so just find x:
3x = 5x - 32

Subtract 5x from both sides:
3x = 5x - 32
   -5x
-2x = -32

Divide both sides by -2:
-2x = -32
/-2     /-2
x = 16

Now just plug it into your equation:
∠PTS = 5(16) - 32
∠PTS = 80 - 32
∠PTS = 48°

To find ∠PTU, subtract ∠PTS from 180:
∠PTU = 180 - 48
∠PTU = 132°

Now for ∠QTP:
Subtract ∠QTU from ∠PTU. ∠QTU = 89 because of corresponding angles:
∠QTP = 132 - 89
∠QTP = 43°