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:

(i) Draw ∠AOB = 80° with the help of protractor.

(ii) With centre O and any radius, draw an arc, meeting  `vec(OB)` and `vec(OB)` at P and Q respectively.

(iii) With centres P and Q and radius more than `1/2hat(PQ)`, draw arcs which cuts each other at R.

(iv) Join OR which bisects PQ at S.

(v) With centres P and S and radius more than `1/2hat(PS)`, draw arcs which cuts each other at U.

(vi) Join OU.

(vii) With centres Q and S and radius more than `1/2hat(QS)`, draw arcs which cuts each other at V.

(viii) Join OV. Thus, ∠AOV, ∠VOR, ∠ROU and ∠UOB divide ∠BOA in four equal parts and ∠AOV = ∠VOR = ∠ROU = 20°