Question

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

• A. 27°
• B. 63°
• C. 90°
• D. 153°

Answer 1

The correct option is A 27°

∠ABC = ∠ADC (Opposite angles of a rhombus)
∠ADC = 126°
∠ODC = $\frac{1}{2}$ × ∠ADC (Diagonal of rhombus bisects the respective angles)
⇒ ∠ODC = $\frac{1}{2}$ × 126° = 63°
⇒ ∠DOC = 90° (Diagonals of a rhombus bisect each other at 90°)

In ΔOCD,
∠OCD + ∠ODC + ∠DOC = 180° (Angle sum property)
⇒ ∠OCD + 63° + 90° = 180°
⇒ ∠OCD + 153° = 180°
⇒ ∠OCD = 180° – 153° = 27°
Hence ∠OCD or ∠ACD = 27°