Answer:
64.5°
Step-by-step explanation:
Using the inscribed angle theorem here would help to find the value of x°.
The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.
First find the arc PM. Write an equation to show that the measures of the following arcs: PQ, QM, and PM add up to 360°, since they span an entire circle. Then solve for the arc PM.
mPM + mPQ + mQM = 360°
mPM + 113° + 118° = 360°
mPM + 231 = 360°
mPM = 129°
Now, find m<Q. <Q is an inscribed angle that intercepts the arc PM, so use the Inscribed Angle Theorem.
m<Q = 1/2 * mHJ
= 1/2 ( 129 )
= 64.5°
X = 64.5 degrees.
