Question

Bisect a right angle, using ruler and compasses. Measure each part. Bisect each of these parts what will be the measure of each of these parts?

Answer 1

Construct right angle

• Draw a line l and mark a point O on it.
• Take O as centre, draw angle of measure 90 degree using protractor. [ As measure of right angle is equal to 90 degree]

Construct angle bisector to the right angle.

• Now, with the centre O, draw an arc with a suitable radius such that it intersects both rays at A and B.
• Now, take A and B as centres and draw arcs with radius more than half of AB such that they intersect each other at interior of angle.
• Let the intersection point of these arcs be C. Now join OC.

Measure each bisected part

Construct angle bisector to ∠AOC

• With A and D as centres, draw arcs of radius more than half of AD such that they intersect each other at interior of ∠AOC.
• Similarly with the same radius, and considering D and B as centres draw arcs, they intersect each other at interior of ∠COI
• Let these arcs intersect at interiors of ∠AOC and ∠COI at E and F respectively.
• Join EO and FO.

• Thus, rays OF, DC and OE divides the given angle into four equal parts.