Question

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

The value of x is:

• A. 45°
• B. 30°
• C. 20°
• D. 15°

Answer 1

The correct option is D

15°

ABCD is a square …...(given)

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

$\angle$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)

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

$\angle$BCE = $\angle$BCD + $\angle$ECD

= 90° + 60°

= 150°

BCE is isosceles …. (from (v))

x + x + 150° = 180°

2x = 30°

x = 15°