# Construction of Angles

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• Q1

Draw an angle of measure 63 with the help of a protactor and draw its angular bisector.

Marks:2

Step 1: With the help of a protactor, draw PAQ = 63

Step 2: With A as the centre , draw an arc that cuts both rays of PAQ. Label the points of intersection as B and C.
Step 3: With B as the centre, draw an arc in the interior of PAQ with a radius of more than half the length BC.

Step 4: With the same radius and with C as centre, draw another arc in the interior of PAQ. Let both the arcs intersect at D. Then is the required bisector.

• Q2

Define angle bisector.

Marks:1

Bisector of an angle means drawing a ray in the interior of the angle with its initial point at the vertex of the angle such that it divides the angle into two equal parts.

• Q3

Construct an angle of 15° with help of a compass and a ruler. Write the steps of construction.

Marks:3

Steps of construction:
1. Draw a line segment of any length.
2. Mark an arc of any radius with centre A, which cuts AB
at Q.
3. Draw another arc of same radius and with centre at Q,
which cuts first arc at P.
4. Draw bisector AR of
PAB.
5. Again draw bisector AC of
RAB.
6.
CAB is required 15°angle.

• Q4

Construct an angle of 105° with help of a compass and a ruler. Write the steps of construction.

Marks:5

Steps of construction:
1. Draw a line segment AB of any length.
2. Draw an arc of any radius with centre at A, which cuts
AB at P.
3. Draw another arc with same radius and centre at P,
which cut first arc at Q.
4. Draw another arc with same radius and centre at Q,
which cuts first arc at R. Join CA through R.
5. Draw two arcs with centres Q and R respectively which
intersect at S. Join A and S.
6. Draw AT as bisector of
CAS.
7.
TAB is required 105°angle.

• Q5

Construct an angle of measure 90 using ruler and compasses.

Marks:2