QPOR is a quadrilateral, and as such, the sum of its interior angles is 360°. We have information about all its angles:
- Angle P is 18*
- Angle R is 30°
- Angle O is [tex] 360-x[/tex], because it is explementary to x
- Angle Q is [tex] \frac{x}{2} [/tex], becuase it is a circumference angle sharing the same arc with angle POR.
So, you have
[tex] x+\dfrac{x}{2}+18+30 = 360 \iff \dfrac{3x}{2} = 312 \iff 3x = 624 \iff x = 208 [/tex]
