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Question

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

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Solution

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.

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