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Question

In the figure below, ΔABC is anequilateral triangle and EC = CD. What is the measure of EDC?


A

60

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B

50

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C

40

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D

30

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Solution

The correct option is D

30


Since ΔABC is equilateral, ABC=ACB=CAB=60.

By exterior angle property in CDE,ACB=CED+EDC(1)

Since CE = CD, CDE is isosceles.

Angles opposite to equal sides areequal in an isosceles triangle.
CED=EDC

Substituting in equation (1), we getACB=2EDC60=2EDCEDC=602EDC=30


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