Question

What is the value of the unknown angle (θ) in the following diagram?

• A. ${120}^{\circ }$
• B. ${70}^{\circ }$
• C. ${90}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is B ${70}^{\circ }$

Using Laws of reflection: $\angle i=\angle r$​,
$\angle N_{1}AB={20}^{\circ }$
Since$N_1$A is the normal,​
$\angle N_{1}AB+\angle OAB={90}^{\circ }$
${20}^{\circ }+\angle OAB={90}^{\circ }$
$\angle OAB={70}^{\circ }$

Sum of angles of triangle is ${180}^{\circ }$
$\angle OAB+\angle OBA+\angle AOB={180}^{\circ }$
${70}^{\circ }+\angle OBA+{90}^{\circ }={180}^{\circ }$
$\angle OBA={20}^{\circ }$

Since $N_2$B is the normal,​
$\angle OBA+\angle AB{N}_2={90}^{\circ }$
${20}^{\circ }+\angle AB{N}_2={90}^{\circ }$
$\angle AB{N}_2={70}^{\circ }$