Question

If ABCD is a rhombus with ∠ABC = 56°, find the measure of ∠ACD.

Answer 1

In a rhombus ABCD, 

∠ABC = 56° 

So, ∠BCD = 2 (∠ACD) (Diagonals of a rhombus bisect the interior angles) 

or ∠ACD = 1/2 (∠BCD) …..(1) 

We know, consecutive angles of a rhombus are supplementary. 

∠BCD + ∠ABC = 180° 

∠BCD = 180° – 56° = 124° 

Equation (1) ⇒ ∠ACD = 1/2 x 124° = 62°