Question

What is the value of the unknown angle $\left(\theta \right)$ in the following diagram?

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

Using Laws of reflection, $\angle N_{1}AB={30}^{\circ }$
Since $N_{1}A$ is the normal,
$\angle N_{1}AB+\angle OAB={90}^{\circ }$
${30}^{\circ }+\angle OAB={90}^{\circ }$
$\angle OAB={60}^{\circ }$
Sum of angles of triangle is ${180}^{\circ }$.
$\angle OAB+\angle OBA+\angle AOB={180}^{\circ }$ ${60}^{\circ }+\angle OBA+{90}^{\circ }={180}^{\circ }$
$\angle OBA={30}^{\circ }$
Since $N_{2}B$ is the normal,
$\angle OBA+\angle AB{N}_2={90}^{\circ }$
${30}^{\circ }+\angle AB{N}_2={90}^{\circ }$
$\angle AB{N}_2={60}^{\circ }$
Using laws of reflection,
$\theta =\angle AB{N}_2$
$\theta ={60}^{\circ }$