Question

In the figure (not drawn to scale), $ABC$ is a straight line, $\angle DBE$ is a right angle and $\angle a=\angle b=\angle c=\angle d$. Find $\angle a$.

• A. ${22.5}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is A ${22.5}^{\circ }$

We have, $\angle a=\angle b=\angle c=\angle d=x$ (say)
Now, $\angle a+\angle b+\angle c+{90}^{\circ }+\angle d={180}^{\circ }$ (Angles on a straight line)
$\therefore x+x+x+{90}^{\circ }+x={180}^{\circ }\Rightarrow 4x={90}^{\circ }$
$\Rightarrow x=\frac{{90}^{\circ }}{4}={22.5}^{\circ }\therefore \angle a={22.5}^{\circ }$.