Question

The bisectors of which of the following angle pairs can include an angle of ${30}^{\circ }$(assuming the angle pair shares a common arm)?

• A. ${60}^{\circ }$ and ${120}^{\circ }$
• B. ${30}^{\circ }$ and ${60}^{\circ }$
• C. $0^{\circ }$ and ${90}^{\circ }$
• D. $0^{\circ }$ and ${60}^{\circ }$

Answer 1

Answer: (A), (D)

The correct options are
A ${60}^{\circ }$ and ${120}^{\circ }$
D $0^{\circ }$ and ${60}^{\circ }$

Consider the angle pair ${60}^{\circ }$ and ${120}^{\circ }$

Lets assume the common arm on +x axis

$\therefore$ The bisectors will form an angle of $\frac{{60}^{\circ }}{2}={30}^{\circ }$ and $\frac{{120}^{\circ }}{2}={60}^{\circ }$ respectively with x axis.

Angle between the Bisectors $={60}^{\circ }-{30}^{\circ }={30}^{\circ }$

which can also be realised as $\frac{\text{difference of angles}}{2}$

The options $B$ and $C$ gives ${15}^{\circ }$ and ${45}^o$ angle

between the bisectors

Similarly in option $D$

Difference $={60}^{\circ }-0^{\circ }={60}^{\circ }$

Angle between the bisectors $=\frac{{60}^{\circ }}{2}={30}^{\circ }$

So option $A$ and $D$ given ${30}^{\circ }$ angle on bisection

Note that if the non common arms lie on the opposite sides of the common arms then Angle between the bisectors will be $\frac{\text{sum of angles}}{2}$ and the value will be ${90}^{\circ }$, ${45}^{\circ }$, ${45}^{\circ }$ and ${30}^{\circ }$ respectively for options A,B,C and D respectively

Hence the correct answer is A and D