Question

Draw an angle of 60° using ruler and compasses and divide it into four equal parts. Measure each part.

Answer 1

Step 1: Construct angle of 60°

Step 2: Construct bisector to ∠RPQ

• With P as centre, draw an arc of radius more than the half of AB such that it intersects rays PR and PQ at A and B respectively.
• Without disturbing the radius of compass, taking A and B as centres draw arcs which intersects each other the interior of the angle at D.
• Join PD.
• 

Step 3: Construct bisector to ∠RPD and ∠DPQ

• Now set the radius of compass as more than half of AC.
• With A and C as centres. Draw arcs such that they intersect each other at interior of angle APD.
• Let us name the intersection point as E.
• Similarly, without disturbing the radius of compass draw arcs considering C and B as centres.
• Let these arcs intersect at F.
• Join PE and PF.
• Thus, PD, PE, PF divides the angle 60° into four equal parts.From this construction, we can observe that perpendicular bisector DE passes through the centre of the circle.

On measuring the divided parts.