Thread: Angles in circle

thank you

Hi -

This is a bit tricky. You need to suppose angle FCD = x. Then angle BCE is also x (vertically opposite angles).

Then you can use the following facts to find an equation for x:

• The exterior angle of a triangle is equal to the sum of the interior opposite angles. (So, for instance, angle ADC = 32 + x)
• The opposite angles of a cyclic quadrilateral are supplementary. (So, for instance, angle ADC + angle ABC = 180 degrees.)

When you've got x you can now use the fact that:

• The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle. (So, for instance, angle DAB = angle FCD.)

I hope you can work it out from here.

Grandad