Question

ABCD is a rhombus,if ,angle ABC =68°, determine angle ACD.

Answer 1

In a rhombus,
Angle ABC + Angle BCD = 180
Hence, BCD = 180-68 = 112.
Now,
The diagonals of a rhombus bisects the angles at its end points.
Therefore,
Angle BCD is bisected by the diagonal AC.
Therefore,
Angle ACD = Angle BCD/2
= 56°
Hence, Angle ACD = 56° Ans.

Answer 2

We know that consecutive angles of a Rhombus are always supplementary.

∠BCD = 180°- ∠ ABC

              = 180° - 68° = 112°

∴∠BCD = 112°

Diagonals of a Rhombus bisects the interior angles.

∠ACD =∠ BCD ÷ 2

           = 112 ÷2

            = 56°

∴∠ ACD = 56°

Ans :- The measurement of  angle ACD is 56°