Question

In the adjoining figure, $AC\perp OC\text{and}AD\perp OD$. Find $\angle CAD$

Answer 1

Here, $ACOD$ is a quadrilateral.

$\angle ADO={90}^o,\angle DOC={75}^o,\angle OCA={90}^o$

We know that, in quadrilateral sum of four angles is ${360}^o.$

$\Rightarrow$ $\angle ADO+\angle DOC+\angle OCA+\angle CAD={360}^o.$

$\Rightarrow$ ${90}^o+{75}^o+{90}^o+\angle CAD={360}^o.$

$\Rightarrow$ ${255}^o+\angle CAD={360}^o.$

$\Rightarrow$ $\angle CAD={360}^o-{255}^o.$

$\therefore$ $\angle CAD={105}^o.$