13. What you want to do is solve for X. However, you need to create an equation that will let you do this.
First, we know the measures of each of the angles (sort of)
ZST=X+120
RST=136
RSZ=X+36
Because angle RSZ is "inside of" or "contained in" angle RST, angle RSZ + angle ZST = angle RST.
Since we know the values of all of these, we can create our equation.
RSZ + ZST = RST
(X+36) + (X+120) = 136
Now, because everything is addition, we can drop the parentheses.
X+36+X+120=136
Now, we add like terms.
X+X+36+120=136
2X+156=136
We now subtract and divide so that we can solve for X.
2X+156=136
2X+156-156=136-156
2X=-20
2X/2=-20/2
X=-10
Now that we have solved for X, we can solve for ZST.
ZST=X+120
ZST=(-10)+120
ZST=110°
I have to post this now, or the time will run out. I will try #14 after posting this.
14. In the same way that RST "contained" the other two angles in 13, IJK contains the other two angles in this one. This means that you need to set IJK equal to the other two angles.
AJK+IJA=IJK
44+(2X+16)=9X-10
Now, to solve for X, we get all of the X's on one side.
44+(2X+16)=9X-10
44+2X+16=9X-10
44+16+2X-9X=9X-9X-10
44+16-7X=-10
60-7X=-10
Now we subtract 60 from both sides to get X by itself.
60-60-7X=-10-60
-7X=-70
We can now divide by -7 to solve for X.
(-7X)/(-7)=(-50)/(-7)
X=+70/7
X=10
Now we can substitute X for 10 and solve for IJK.
IJK=9X-10
IJK=[9(10)]-10
IJK=(90)-10
IJK=80
