Question

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

Answer 1

Please refer to the attached pic

Answer 2

Given :  ABCD is a rhombus with ∠ABC = 56°.

To prove :  Measure of ∠ACD.

 

Proof :  

we have, a rhombus ABCD,  

So, ABCD is a parallelogram .

∠ABC = ∠ADC =  56°

[Opposite angles of a parallelogram are equal]

∠ADC =  56°

∠ODC =  ½ × 56°

[Diagonals of a rhombus bisect the interior angles, ∠ODC =  ½ × ∠ADC]

∠ODC =  28°

Now, ∆OCD ,we have

∠OCD + ∠ODC + ∠COD = 180°

∠OCD + 28° + 90° = 180°

[∠COD = 90° , diagonals of a rhombus bisect each other at right angles]

∠OCD + 118°  = 180°

∠OCD   = 180° - 118°

∠OCD   = 62°

∠ACD   = 62°

Hence, the measure of ∠ACD is 62°.  

HOPE THIS ANSWER WILL HELP YOU…..

 

Similar questions :

ABCD is a rectangle with ∠ABD=40°. Determine ∠DBC.

https://brainly.in/question/15909379

 

In a parallelogram ABCD, if ∠D=115°, then write the measure of ∠A.

brainly.in/question/15909396