Question

ABCD is rhombus with ∠ABC = 30°. The measure of ∠ACD is:

• A. ${60}^{\circ }$
• B. ${75}^{\circ }$
• C. ${150}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is B

${75}^{\circ }$

∠ABC = ${30}^{\circ }$ (Given)
A rhombus is also a parallelogram.

Hence ∠BCD = ${180}^{\circ }$ - ${30}^{\circ }$ = ${150}^{\circ }$ (Adjacent angles of a parallelogram are supplementary)

$\because$ Diagonals of rhombus bisects the angles.

$\therefore$ ∠ACD = $\frac{1}{2}$ ∠BCD
= $\frac{1}{2}$ × ${150}^{\circ }$
= ${75}^{\circ }$