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# Construction of Angles

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Construction of copy of an angle:

An exact copy of a line segment can be constructed using a ruler and a compass.

• Construction of a copy of an angle YXZ.
• Draw a line AB.
• Mark any point O on AB.
• Place the compass pointer at vertex X of the given figure and draw an arc with a convenient radius, cutting rays XY and XZ at points E and F, respectively.
• Without changing the compass settings, draw an arc on line AB from point O. It cuts line AB at P.
• Set the compass to length EF.
• Without changing the compass settings, draw an arc from P cutting the previous arc at point Q.
• Join points O and Q.
• Hence, ∠POQ  is the required copy of ∠YXZ.

Construction of the bisector of an angle:
• Construction of the bisector of an angle LMN.
• Place the compass pointer at vertex M of the given angle.
• Draw an arc cutting rays ML and MN at U and V respectively.
• Draw an arc with V as the centre and a radius more than half the length of UV in the interior of ∠LMN.
• Draw another arc with U as the centre and the same radius intersecting the previous arc.
• Name the point of intersection of the arcs as X.
• Join points M and X.
• Ray MX is the required bisector of ∠LMN.

Construction of a 60° angle:

• Draw a line.
• Mark a point P on the line.
• Draw an arc from point P with a convenient radius cutting the line at a point.
• Name the point of intersection of the arc and the line as Q.
• Draw another arc with Q as the centre and the same radius so that it passes through point P.
• Name the point of intersection of the two arcs as R.
• Join points P and R.
• Ray PR forms an angle with ray PQ at point P, which measures 60°.
• ∠QPR is the required angle measuring 60°.

Construction of a 30° angle:

• To obtain a 30° angle, we need to bisect a 60° angle.
• Draw an arc with Q as the centre and a radius more than half the length of QR.
• Draw another arc with R as the centre without changing the compass settings so that it intersects the previous arc.
• Name the point of intersection of the arcs as S.
• Join points P and S.
• ∠QPS is the required angle measuring 30°.

In a similar way, we can construct a 120° angle and 90° angle without using the protractor.

Construction of a 120° angle
• Draw line XY.
• Mark a point on the line and name it as P.
• Draw an arc with P as the centre and a convenient radius so that it cuts the line at Q.
• Draw another arc with Q as the centre without changing the compass settings so that it intersects the first arc at R.
• Draw another arc with R as the centre without changing the compass settings so that it intersects the first drawn arc at point S.
• Join points P and S.
• ∠SPQ is the required angle measuring 120°.

Construction of a 90° angle

• Draw line l and mark point P on it.
• Draw an arc with P as the centre and a convenient radius cutting line l at Q.
• Draw another arc with Q as the centre and the same radius cutting the first arc at R.
• Draw an arc with R as the centre and the same radius cutting the first arc at S.
• Join points P and R.
• Join points P and S.
• 90° lies to the centre of 60° and 120°.
• Draw an arc with R as the centre and a radius more than half the length of RS in the interior of ∠RPS.
• Draw another arc with S as the centre and the same radius so that it intersects the previous arc at T.
• Join points P and T.
• PT is the perpendicular line to PQ.
• ∠QPT is the required angle measuring 90°.

### 1 . draw an angle of measure 153 degree

Draw an angle 60 degree and bisect 30

### 2 . how to draw an angle of 153 degree & 147 degree.

To draw 147°  using protractor.

First draw a line segment or a ray OA
Makre O as centre and place t...

### 3 . what did you mean by bisector in maths

Bisector: If a line segment is divided into two equal parts by a line then it is called a bisector of the given line segment.
Angle...