Answer:
x = 84
Explanation:
1. Solve for m<R
The sum of angles in a triangle is 180 degrees, regardless of each individual angle measure in the triangle. One can apply that to triangle QRS by stating that;
m<SQR + m<R + m<QSR = 180
Substitute
68 + 3x + m<R = 180
Inverse operations,
m<R = 112 - 3x
2. Solve or m<PSR
Verticle angles theorem states that when two lines intersect, four angles are formed. The angles that are opposite each other are congruent. Using this, one can concluce that;
m<TSU = m<PSR = 4x
3. Solving for x
Now all one has to do is apply the sum of angles in a triangle theorem for triangle PSR
m<P + m<R + m<PSR = 180
Substitute,
x + 112 - 3x + 4x = 180
Simplify
2x + 112 = 180
Inverse operations
2x + 112 = 180
-112 -112
2x = 168
/5 /5
x = 84