Question

In the given figure, ABCD is a square. Find the measure of $\angle CAD$.

Answer 1

In square ABCD, AC is its diagonal.

We know that, the diagonals of a square bisect the interior angles.

$\therefore \angle CAD=\angle CAB$

But, $\angle DAB={90}^{\circ }\text{(Angle of a square is 90^circ)}$

$\therefore \angle CAD=\angle CAB=\frac{1}{2}\times \angle DAB$

= $\frac{1}{2}\times {90}^{\circ }={45}^{\circ }$

Hence, $\angle CAD={45}^{\circ }$