Question

Which of the following angles can be constructed without using a protractor?

• A. 30${}^{\circ }$
• B. 40${}^{\circ }$
• C. 50${}^{\circ }$
• D. 60${}^{\circ }$

Answer 1

Answer: (A), (D)

60${}^{\circ }$

Angles 60${}^o$ and 30${}^o$ can be constructed using a scale and compass.
1. Draw a line l.
2. With O as centre and with any convenient radius, draw an arc to cut line l at A.
3. With A as centre and with the same radius, draw an arc to cut the previous arc at B.
4. Join OB and extend. $\angle AOB={60}^o$

5. To construct 30${}^o$ we bisect 60${}^o$.
The remaining two angles cannot be constructed without using a protractor.