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1
5. Fold the semicircle sheet in half to form a quarter circle. This is th of the circle = 90°.
4
90°
Fold
180° 0° 180° 0°
1
6. Fold the sheet again. This is th of the circle, so one crease will be at 45° and the other at 135°.
8
90°
135°
45°
180° 0°
7. Repeat the process once again and unfold it. Mark the creases as OA, OB, OC, OD, ....., OI.
F E D 112.5° 90° 67.5°
G C 135° 45°
H B 157.5° 22.5°
I A 180° 0°
O
1 °
Here, a semicircle is divided into 8 equal parts. So, ∠AOB = ∠BOC = ∠COD = ... = ∠HOI = 22
or 22.5°. 2

Angle Bisector Quick Check

At each step, we folded the paper in halves. This Looking the given figure, fill in the blanks.
process of dividing a given angle in half is called T
bisecting the angle. The line that bisects a given S
angle is called the angle bisector of that angle. R

Identify the angle bisectors in your handmade 30° 15° Q
protractor. For your reference, OB is the angle 15°
bisector of ∠AOC. Similarly, OC is the angle is O 30° P
bisector of ∠AOE. 1. ............... is the angle bisector of ∠QOS.
Drawing Angles 2. OS is the angle bisector of ............... and
............... is the angle bisector of ∠POT.
Nishtha wants to draw ∠ABC using a protractor and a ruler, but she is not able to draw the correct
angle. She takes help from her mother. Here are the steps that Nishtha’s mother told her. Let us
look how she explains to draw an angle measuring 70°.

1. Draw a ray AB. It will be the base of the angle.
A B
2. Place the centre of the protractor at point A such that its zero edge lies along the ray AB.

47 Lines and Angles