Hello, Natasha!

Some basic geometry (plus a little algebra) is required.

A cyclic hexagon is a hexagon whose vertices all lie on the circumference of a circle.

The vertices of a cyclic hexagon are labelled in order A to F.

Prove that the sum of the interior angles at A, C and E

is equal to the sum of the interior angles at B, D and F. Code:

A
* o *
* o o *
F o o B
*o o*
o o
* o o *
* o * o *
* o o *
o o
*o o*
E o o C
* o o *
* o *
D

An inscribed angle is measured by one-half its intercepted arc.

. .

. .

. .

Then: .

Hence: .

In a similar fashion, it can be shown that: .