Math CentralQuandaries & Queries


O is the center of the circle.  Sides AB and AE are equal.  Angle B = 95, angle C = 130, angle D = 138.  Find angles A and E.


Faisal's diagram

Faisal's diagram


The theorem you should try to use here:

BCDE is a quadrilateral inscribed in a circle so the sum of the angles at B and D add up to 180 degrees.

To set the theorem up, set the angle at A equal to x degrees. Then in the isosceles triangle ABE you can figure out the measure of the equal angles at B and E in terms of x. Subtract that number from the total angle of the pentagon at B (namely 95 degrees) and you get the portion of the angle B that lies in the quadrilateral BCDE. Add the resulting number to angle D = 135; the total must be 180 degrees, so you have an equation that you can solve for x.


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