Need some geometry help!?

Question

Yes, well math was never my forte and I need some help answering a couple of questions. Thanks for your time

Rays ST and TV are perpendicular. Point Z lies in the interior of STV. If m VTZ = 4c + 9 and m ZTV = 3 + 9c, find m VTZ and m ZTV.

and

If R and S are complementary and m R = 5x + 8 and
m S = x + 4. Find m R and m S.

explain please thanks. :)

Answer 1

some definitions to start:

perpendicular means the two segments for a right angle.
angles are usually designated by three letters (the second problem deviates from this)
m VTZ should mean the measure of angle VTZ
complementary means the angles add up to 90 degrees

The first problem:

If the rays are perpendicular, this means a right angle is formed meeting at a vertex called T. Point Z is inside the angle allowing for the right angle to be split into two smaller angles. (VTZ and ZTS) these two angles must equal 90 degrees.

so:
VTZ + ZTS = 90
(4c+9) + (3+9c) = 90
4c+9c+9+3=90
13c+12=90
13c=78
c=6

if VTZ=4c+9 and c=6 then 4(6)+9=33
the measure of angle VTZ is 33, this means the measure of ZTS must be 57 (just plug 6 into 3+9c)

Problem 2:
This problem differs in its set up but is solved the same way. Instead of using three letters to name each angle it simply names the angles R and S. They are however complementary so we will solve in the same way:
angle R+angle S=90
(5x+8)+(x+4)=90
5x+x+8+4=90
6x+12=90
6x=78
x=13

So angle R is:
5x+8
=5(13)+8
=73

Angle S must be 17

enjoy!

Answer 2

Rays ST and TV are perpendicular. Point Z lies in the interior of STV. If m VTZ = 4c + 9 and m ZTV = 3 + 9c, find m VTZ and m ZTV.

VTZ = ZTV (they are two ways of describing the same angle)
4c +9 = 3 + 9c
6 = 5c
1.2 = c
m VTZ = 4(1.2) + 9 = 4.8 +9 = 13.8

However, I think the problem involves VTZ and ZTS, which are two angles that add to 90 degrees (since they are perpendicular), and is written wrong.
m VTZ + m ZTS = 90 degrees
(4c +9) + (3 + 9c) = 90
13c + 12 = 90
13c = 78
c = 6
Plugging c into the equations
VTZ = 4c+9 = 4(6) +9 = 33 degrees
ZTS = 3+9c = 3 + 9(6) = 57 degrees


Problem 2:
If R and S are complementary and m R = 5x + 8 and
m S = x + 4. Find m R and m S.

Complementary angles add to 90 degrees
mR + mS = 90
(5x+8) + (x+4) = 90
6x + 12 = 90
6x = 78
x = 13
Plugging into the equations
mR = 5x+8 = 5(13) +8 = 73 degrees
mS = x+4 = 13 + 4 = 17 degrees