Question

An angle of measure $15°$ can be constructed by using ruler and compass if an angle of:

• A. $30°$ is bisected
• B. $45°$is bisected
• C. $60°$ is bisected
• D. none of these

Answer 1

The correct option is A

$30°$ is bisected

We know that the angle bisector divides the angle into two equal parts.

So, if a $30°$ angle is bisected it will give two equal angles of $\frac{30}{2}=15°$.

Hence, an angle of measure $15°$ can be constructed by using ruler and compass if an angle of $30°$ is bisected.

Explanation for the incorrect options:

Option (B) $45°$ is bisected

We know that the angle bisector divides the angle into two equal parts.

So, if a $45°$ angle is bisected it will give two equal angles of $\frac{45}{2}=22.5°$.

Hence, an angle of measure $15°$ can not be constructed by using ruler and compass if an angle of $45°$ is bisected.

Option (C) $60°$ is bisected

We know that the angle bisector divides the angle into two equal parts.

So, if a $60°$ angle is bisected it will give two equal angles of $\frac{60}{2}=30°$.

Hence, an angle of measure $15°$ can not be constructed by using ruler and compass if an angle of $60°$ is bisected.

Hence, the correct option is option (A).