Question

In the given figure; ABCD is a rhombus with A = 67° .
if DEC is an equilateral triangle , calculate
(i) CBE
(ii) DBE​

Answer 1

Explanation :

In rhombus ABCD angle A and angle C are equal (In a rhombus opposite a glass are equal.)

Therefore angle C is equal to 67 degrees.

In triangle CDB,

CD=BC (all sides are equal)

Therefore it is isosceles.

Now to find angle CDB,

67 +2x=180

2x=180-67=113

Therefore x=56.5 degrees

Similiarly in triangle ABD,

angle ADB=56.5 degrees

Therefore Angle CDA=56.5+56.5 =113 degrees.

But, angle CDA forms a linear pair with Angle CDE=60 degrees (equilateral triangle)

And 113 + 60 is not equal to 180 degrees.

Therefore I think the question is not correct.

Kindly comment if I have gone wrong somewhere.