Question

Quadrilateral OPQR is inscribed in a circle as shown below...

Answer 1

We can use the fact that a cyclic quadrilateral (i.e. a quadrilateral inscribed in a circle) has the opposite angles supplementary, therefore
2x+(2x+4) = 180
Solving for x:
4x+4=180 
4x=180-4=176
x=176/4=44 °
=>
angle O = 2x = 88 °  
angle Q=180-O=180-88 = 92 °

Similarly,
(3y+8)+y= 180
=> y=43 °
=>
P=y=43 °
R=180-43=137 °