Question

You are asked to "construct" an angle whose measure is ${30}^{\circ }$. Which of the following methods would be considered as an acceptable construction?

• A. Using a compass and straightedge, construct two parallel lines and label one of the angles ${30}^{\circ }$.
• B. Using a compass and straightedge, construct an equilateral triangle and then bisect one of its angles.
• C. Using a compass and straightedge, copy an angle that appears to be close to ${30}^{\circ }$ from a diagram in your textbook.
• D. None of these

Answer 1

The correct option is B Using a compass and straightedge, construct an equilateral triangle and then bisect one of its angles.

We only need to construct an angle of ${30}^o$.

We have not been provided with any side or point.

So, its best to construct an equilateral triangle by drawing ${60}^{\circ }$ angles and then extending and joining them with the straighedges

Since every angle is of measure ${60}^o$, so bisecting one of the angle will form an angle of measure ${30}^o$.

Hence, the acceptable construction is given by option B.