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4. Join PR with the help of a ruler.

Thus, ∠QPR = 114° is the required angle.

Bisecting an Angle

An angle can be bisected:

(a) By protractor (b) By paper folding (c) By ruler and compass
To bisect means to divide into two equal parts. Let us understand the bisection by all the methods
mentioned above.
X
(a) Bisection of an angle using a protractor

Suppose we have to bisect an angle, say ∠XOY = 60°.

60°
l Divide the angle measure by 2 i.e., = 30°. 60°
2 O Y
l Place the vertex of angle O at the centre of the protractor and mark a point (say Z) in the
interior of angle at 30°.
X
l Join O with the marked point Z.

l Hence, OZ is the angle bisector of ∠XOY. Z
Thus, ∠XOZ = ∠ZOY = 30°. 30°
O 30° Y
(b) Bisection of an angle using paper folding
A
Paper folding is a great way to learn mathematical concepts with visual
practical experience by students. Suppose we have an angle ∠ABC made
on a piece of tracing paper.

l The paper containing the angle is folded so that the ray BC of ∠ABC B C

overlaps the ray BA .
l When unfolded, the fold line is the angle bisector.

A A(C) A

Fold line
B B B
C C

49 Lines and Angles