Question

In the adjoining figure, $ABCD$ is a rhombus and $\angle ABD={50}^{\circ }$ . Find

• A. $\angle CAB$
• B. $\angle BCD$
• C. $\angle ADC$
• D. $\angle DAC$

Answer 1

The correct option is A $\angle CAB$

Diagonals bisect the angles at vertices

$⟹\angle ABD=\angle DBC={50}^{\circ }\angle ABC={100}^{\circ }$

The adjacent angles sum up to give ${180}^{\circ }$

$⟹\angle DAB+\angle ABC=180\angle DAB=180-\angle ABC\angle DAB=180-100={80}^{\circ }⟹\angle CAB={40}^{\circ }\angle DAC={40}^{\circ }$

The opposite angles are equal $⟹\angle DAB=\angle BCD={40}^{\circ }$

The opposite angles are equal $⟹\angle ADC=\angle ABC={100}^{\circ }$