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

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Dan L. Share
Mar 8, 2018

Answer:

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#

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