Quadrilateral opqr is inscribed inside a circle as shown below. what is the measure of angle q? you must show all work and calculations to receive credit.

To solve the question we must first assess known facts about the angles of a square:
The sum of the angles in a square is equivalent to 360 degrees.
The opposite angles in a square are always equivalent to 180 degrees.

To begin solving the problem, lets first set up the equation:
4y + 8 = 180
Angle R + Angle P = 180 degrees by Opposite Angles Quadrilateral Conj.

The equation solves as:
y=43

To solve for the value of x we must set up the equation:
4y+4x+12=360
Then substitute y:
4(43)+4x+12=360

172+4x+12=360
4x=176
x=44

The value of X is 44 and the value of Y is 43

To find the measure of angle Q we must simply substitute:
2x+4 
88+4
92 

92 is the measure of angle Q

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