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7. Join PQ and extend. This gives us ∠PQR. It

has the same measure as ∠ABC.
P

Q R

Construction of the Bisector of a Given Angle

To bisect an angle, we draw a ray in the interior of the angle so that the angle is divided into two

equal parts. Let us take an ∠AOC.
Steps of construction:

1. With O as a centre and using compass, draw 2. With Y as the centre, draw an arc (in the
an arc that cuts both rays of ∠O. Label the interior of ∠O) whose radius is more than
points of intersection as X and Y. half the length of XY.
A A
X X

O O
Y C Y C
3. With the same radius and with X as the centre, draw another arc in the interior of ∠O. Let

the two arcs intersect at Z. Then OZ bisects ∠AOC. Therefore, ∠AOZ and ∠ZOC are equal.
A
X
Z

O
Y C

activity
Take a small piece of paper and draw an angle on it. Fold the sheet through the centre of
the angle such that the rays overlap and press the two parts such that a crease is formed in
the middle. Draw a line through the crease. This line is the angle bisector of the given angle.

Construction of Angles of Special Measures (30°, 45°, 60°, 90°,

120°, etc.)

There are some elegant and accurate methods to construct some angles of special sizes, i.e., angles
whose measure is a multiple of 15°, which does not require the use of the protractor.

You have learnt the construction of any given angle using a protractor. Now, we will learn
construction of some angles using compass only.

Mathematics-7 340