Question

$ABCD$ is a rhombus in which diagonals $AC$ and $BD$ intersect each other at $O$ . If $\angle ACD={55}^{\circ }$ find $\angle BDC$

Answer 1

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

$\angle ADC+\angle BCD=180\frac{1}{2}\angle ADC+\frac{1}{2}\angle BCD={90}^{\circ }$

Diagonals bisect the angles

$⟹\angle BDC+\angle ACD=90\angle BDC=90-55={45}^{\circ }$