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Question

The value of x in the gi ven figure is


A

60

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B

45

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C

30

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D

15

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Solution

The correct option is C

30


Since ABC is equilateral, we must have A=B=C=60

[In any equilateral triangle, all angles are 60]
ACD=120 [BCA and ACD form linear pair]
ACD is isosceles [ AC=CD, as shown in the figure]
CAD=ADC=x (If two sides of a triangle are equal, the angles opposite these sides are also equal)
In ACD, by angle sum property, wee must have

x+x+120=180

x=(180120)2=30


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