# Circle Geometry Help - Very Difficult

• Sep 8th 2012, 11:05 PM
eskimogenius
Circle Geometry Help - Very Difficult
Hi there,

Need some help with this circle geometry question:

Point P is marked inside a regular hexagon ABCDEF so that Angle BAP = Angle DCP = 50 degrees.

Find the size of angle ABP.

Thanks!
• Sep 9th 2012, 12:03 AM
MaxJasper
Re: Circle Geometry Help - Very Difficult
• Sep 9th 2012, 02:02 AM
eskimogenius
Re: Circle Geometry Help - Very Difficult
Quote:

Originally Posted by MaxJasper

Care to elaborate? What theorems? How did you arrive at that conclusion?
• Sep 14th 2012, 07:46 PM
Tim28
Re: Circle Geometry Help - Very Difficult
We know that the interior angles of a regular hexagon are 120 degrees.
The triangles with apex P are congruent by side-angle-side.
So all the base angles are 50d or 70d.
So angle ABP is 70 degrees
• Sep 14th 2012, 10:37 PM
eskimogenius
Re: Circle Geometry Help - Very Difficult
How do you know that the triangles are congruent? They are most certainly not. Only one side is equal in each of the triangles, that is all you know.