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Question

In ABC,AB=AC. Points D and E are on the sides BC and AC respectively such that AD=AE. If BAD=30, then the measure of EDC is:

A
10
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B
15
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C
20
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D
25
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Solution

The correct option is B 15
Given, AB=AC
B=C=x (Isosceles triangle Property)
Given, AD=AE
D=E=y (Isosceles triangle Property)
Sum of angles =180o
DAC+ADE+AED=180o
DAC=180o2y
In ΔDEC,y is external angle
DEA=EDC+ECD (Exterior angle property)
y=a+xa=yx
In ΔABC,
Sum of angles =180o
ABC+ACB+BAC=180o
2x+30+1802y=180
2(yx)=30
yx=15=a
EDC=15
Hence, option B is correct.
238506_206419_ans_c210778068404d81bea4f641eae77eae.png

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