SOLUTION: ABCDE is a regular pentagon. On AB, a square ABXY is drawn lying within the pentagon. Find the number of degrees in the angles CBX, DCX, and XBD.

Question 1060279: ABCDE is a regular pentagon. On AB, a square ABXY is drawn lying within the pentagon. Find the number of degrees in the angles CBX, DCX, and XBD.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The sides of the pentagon and the sides of the square have all the same length,
so triangle BCX is isosceles, and DCB is isosceles.
because ABXY is a square.
because ABCDE is a pentagon,
with external angles measuring ,
and internal angles measuring .
So, .

Since BCX is isosceles, besides its vertex angle,
it has two base angles measuring
.
Since DCB is isosceles, besides its vertex angle,
it has two base angles measuring

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