Question

In the figure, given below, $ABCD$ is a cyclic quadrilateral in which $\angle BAD={75}^o;\angle ABD={58}^o$ and $\angle ADC={77}^o$. Find: $1)\angle CBD$ $2)\angle BCD$

Answer 1

Given $ABCD$ is a cyclic quadrilateral

We know that in a Cyclic Quadrilateral opposite angles are supplementary.

$⟹\angle ADC+\angle ABC={180}^{\circ }$

$⟹\angle ABC={180}^{\circ }-{77}^{\circ }$

$⟹\angle ABC={103}^{\circ }$

Therefore,$\angle CBD=\angle ABC-\angle ABD$

$⟹\angle CBD={103}^{\circ }-{58}^{\circ }={45}^{\circ }$

And also,

$\angle DAB+\angle BCD={180}^{\circ }$

$⟹\angle BCD={180}^{\circ }-{75}^{\circ }={105}^{\circ }$