Question

Nish wants to find the number of arcs used to construct $\angle ABX={30}^{\circ }$ using only a compass and a ruler after drawing the base ray PX. Help her find the number of arcs she makes with the compass.

• A. 4

Answer 1

The correct option is A 4
Steps of construction:

1. Draw a ray BD.

2. With B as the center and any radius, draw an arc that cuts BD at point C. This is the first arc.

3. With C as the center and the same radius, cut the previous arc at A. This is the second arc.

4. With A as the center and any radius more than half of AC, draw another arc as shown. This is the third arc.

5. With C as the center and the same radius as above, cut the previously drawn arc at E. This is the fourth arc.

6. Join BE.

In the figure shown above, $\angle DBE=\angle ABE={30}^{\circ }$.