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

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#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

2
Dan L. Share
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. $= \frac{x}{2}$)
('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 $360 - x$

So we can form an equation:

$20 + 20 + \frac{x}{2} + \left(360 - x\right) = 360$

By rearranging for $x$, you can show that
$40 - \frac{x}{2} = 0$
$\implies \frac{x}{2} = 40$
$\implies x = 80$

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