Question

Which of the following angles are to be bisected to construct an angle of 105° with the help of compass and ruler?

• A. 60° and 120°
• B. 75° and 120°
• C. 90° and 120°
• D. 90° and 180°

Answer 1

The correct option is C 90° and 120°

If we find the average of a pair of given angles, then we can get the angle which is the bisector of them.
To get 105°, we need to find the pair of angles whose average is 105°.
Calculating the average of given pairs of angles, we get
$\frac{60°+120°}{2}=90°\frac{75°+120°}{2}=97.5°\frac{90°+120°}{2}=105°\frac{90°+180°}{2}=135°$
Therefore, we need to bisect 90° and 120° to get 105°.