Question

Draw an angle of 80° using a protractor and divide it into four equal parts, using ruler and compasses.Check your construction by measurement.

Answer 1

Steps of construction:

1. Draw ∠AOB = 80° with the help of protractor.
2. With centre O and any radius, draw an arc, meeting `vec(OB)` and `vec(OB)` at P and Q respectively.
3. With centres P and Q and radius more than `1/2 (hat(PQ))`, draw arcs which cuts each other at R.
4. Join OR which bisects PQ at S.
5. With centres P and S and radius more than `1/2 (hat(PS))`, draw arcs which cuts each other at U.
6. Join OU.
7. With centres Q and S and radius more than `1/2 (hat(QS))`, draw arcs which cuts each other at V.
8. Join OV. Thus, ∠AOV, ∠VOR, ∠ROU and ∠UOB divide ∠BOA in four equal parts and ∠AOV = ∠VOR = ∠ROU = 20°