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Question

In the given figure, ABCD is a square and DEC is equilateral.

The value of x is:


A

45°

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B

30°

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C

20°

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D

15°

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Solution

The correct option is D

15°


ABCD is a square …...(given)

AB = BC = CD = DA ……. (sides of the square) ……. (i)

BCD = 90° ……. (angle in a square) ……… (ii)

DEC is equilateral …….. (given)

DC = CE = ED (sides of the equilateral triangle) …(iii)

Therefore, from (1) and (iii), EC = CB ….. (iv)

ECD = 60° (angles of an equilateral triangle) ... (v)

BCE = BCD + ECD

= 90° + 60°

= 150°

BCE is isosceles …. (from (v))

x + x + 150° = 180°

2x = 30°

x = 15°

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