Question

In the given figure, if $\angle CAD={150}^{\circ }$ and $\angle ABC={60}^{\circ },$ then reflex $\angle ACB=$___ .

Answer 1

$\angle ACB+\angle ABC=\angle DAC$
[Exterior angle property]
$\angle ACB+{60}^{\circ }={150}^{\circ }\angle ACB={90}^{\circ }\therefore \text{Reflex}\angle ACB={360}^{\circ }-{90}^{\circ }={270}^{\circ }=3\times {90}^{\circ }=3\text{right angles}$