Q. 64.4( 8 Votes )

In the given figure, ΔABC is an equilateral triangle and ΔBDC is an isosceles right triangle, right-angled at D. Then ACD = ?


A. 60°

B. 90°

C. 120°

D. 105°

Answer :

Since we know all the angles in an equilateral triangle is of 60°.

So, ABC = ACB = CAB = 60° …(i)


Also for an isosceles triangle, the angles opposite to equal sides are equal.


So, DBC = DCB = x (lets say)


Also sum of all angles in a triangle = 180°.


So, in ΔBDC,


DBC + DCB + BDC = 180°


x + x + 90 = 180 {since BDC = 90°}


2x = 90


x = 45°


so DCB = 45 (ii)


And ACD = ACB + DCB = 60° + 45° = 105° {from (i) and (ii)}

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