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

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1 Answer
Mar 8, 2018

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