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

Steps of construction:

(i) Draw ∠AOB = 90° with the help of protractor.

(ii) Draw an arc with centre O and any radius, which cuts the ray OB and OA at U and Y.

(iii) With centres U and Y draw the arcs with radius more than `1/2 (hat(UY))`, which cuts each other at Q.

(iv) Join OQ and produce it to any point D as well as it cuts the arc `hat(YU)` at W.

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

(vi) Join OP and produce it to any point E.

(vii) Now with centres Y and W and radius more than `1/2 (hat(YW))` draw the arcs which cuts each other at R.

(viii) Join OR and produce it to any point C. On measuring, we have ∠BOD = ∠AOD = 45° and ∠BOE = ∠EOD = ∠DOC = ∠COA = `22 1/2^circ`