Question

17. ABCD is a rhombus with angle ABC = 126°, find the measure of angle ACD.​

Answer 1

Answer

The measure of ∠ACD is 27°.

Step-by-step explanation:

To Find :-

• The measure of ∠ACD

★ Solution

Given that,

• ABCD is a rhombus.
• ∠ABC = 126°

Firstly, finding the measure of ∠BCD :-

We know,

Adjacent angles of rhombus measures 180°,

Therefore,

• ∠ABC + ∠BCD = 180°

⇒ ∠ABC + ∠BCD = 180

⇒ 126 + ∠BCD = 180

⇒ ∠BCD = 180 - 126

⇒ ∠BCD = 54°

Now, According the question,

We got, ∠BCD = 54°

As we know that,

Diagonals of rhombus bisects the angles of rhombus (interior angles)

• ∴ ∠ACD = ∠BCD ÷ 2

⇒ ∠ACD = ∠BCD/2

⇒ ∠ACD = 54/2

⇒ ∠ACD = 27°

Hence, The measure of ∠ACD is 27°.