Question

I ended up applying all the circle theorem's I knew. Can you help me figure this out?

Answer 1

x=80

Explanation:

You only need one circle theorem for this solution:.
The angle at A (BAC) is half the size of `x` (i.e. `=x/2`)
('The angle subtended by an arc at the centre is twice the angle subtended at the circumference.' Source: BBC Bitesize )

Then some basic geometry:
All angles around a point add up to 360°
So internal angle at P (CPB) can be written as `360-x`

And all angles in a quadrilateral add up to 360°
So we can form an equation:

`20 + 20 + x/2 + (360-x) = 360`

By rearranging for `x`, you can show that
`40-x/2 = 0`
`=> x/2 = 40`
`=> x=80`