Quadrilateral OPQR is inscribed inside a circle as shown below. What equation would be needed to solve for angle P? What is the measure of angle P?

Question

anonymous · Answer

Any help is very much appreciated, I'd like for someone to explain to me, not just give me an answer because I don't understand this. Thank you.

anonymous · Answer

I got 43, is this correct?

zepdrix · Answer

The interior angles of a `quadrilateral` add up to 360 degrees.

So we can add up our angle measures and set it equal to 360.$$\Large\rm (2x)^o+y^o+(3y+8)^o+(2x+4)^o=360^o$$

But if we're not given a value for x, I'm not sure how we can get a numerical solution for y.
Hmmm, what steps did you take to get 43?

anonymous · Answer

These were my steps: 

Angle P + angle R = 180 degrees. 
Angle P = y  and angle R = 3y + 8.
y + 3y + 8 = 180 
4y + 8 = 180

angle p = 43

@zepdrix

zepdrix · Answer

Opposite angles of a quadrilateral inscribed in a circle are supplementary?
Ooo interesting! I didn't know that :)

Your steps look correct!
Yay good job!

anonymous · Answer

Thank you :3