Question

12. Find the value of x. (2 points - 1 point for equation, 1 point for answer)

Answer 1

Answer: x = 7

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Angle STU is 15x. This is the exterior angle on the right side of the triangle
Subtract this from 180 to get angle RTS

angle RTS = 180 - (angle STU)
angle RTS = 180 - 15x

Focus solely on triangle RTS. If needed, erase the portion that extends out toward point U
If we focus on the triangle only, then angle R = angle T since they are the base angles of the isosceles triangle. We know that triangle RST is isosceles since RS = ST is given to us.

Because angle R = angle T, we know 
angle R = 180-15x
angle T = 180-15x
and we also know
angle S = 4x+2
since that's given as well

Add up the three angles and set that sum equal to 180. Then solve for x
R+S+T = 180
(180-15x)+(4x+2)+(180-15x) = 180
(-15x+4x-15x) + (180+2+180) = 180
-26x + 362 = 180
-26x + 362-362 = 180-362
-26x = -182
-26x/(-26) = -182/(-26)
x = 7