Question

How many arcs do we need to construct a ${15}^{\circ }$ angle without using a compass if a ray is given?

• A. 8

Answer 1

The correct option is A 8
Steps of construction:

1. Draw a ray OA.

2. With O as the center and any radius, draw an arc that cuts OA at point P. This is the $firstarc$.

3. With P as the center and the same radius, cut the previous arc at Q. This would be the $secondarc$.

4. With O as the center and any radius more than OP, draw another arc as shown. This is the $thirdarc$.

5. With P as the center and the same radius as above, draw the arc inside the angle ${60}^{\circ }$. This would be the $fourtharc$.

5. With Q as the center and the same radius as above, cut the previously drawn arc at C. This would be the $fiftharc$.

6. Join OC.

7. With O as the center and any radius more than OP, draw another arc as shown. This is the $sixtharc$.

8. With the above arc that touches ray OA as the center and the same radius as above, draw an arc as shown. This would be the $seventharc$.

8. With the above arc that touches ray OC as the center and the same radius as above, cut the previously drawn arc at D. This would be the $eightharc$.

In the figure shown above, $\angle AOD={15}^{\circ }$.