Question

In each of the pictures below, draw aangle, according to the specifications:

(i) At the point A

(ii) At the point A with one side along OA

(iii) At the point A one side along AB

Answer 1

(i)

To construct the required angle at point A, we will use the following property.

Angle made by an arc at any point on the alternate arc is equal to half the angle made at the centre.

The steps of construction are as follows:

(1) Draw a circle of any radius with O as the centre.

(2) Take a point B on the circle and join OB.

(3) Taking O as the centre and OB as the segment, draw an angle of measure 45° such that it intersects the circle at point C.

(Since we need ∠CAB =we have drawn ∠COB = 45°.)

(4) Join CA and AB.

∠CAB is the required angle.

(ii)

To construct the required angle at point A with one side along OA, we will use the following property.

Angle made by an arc at any point on the alternate arc is equal to half the angle made at the centre.

(1) Draw a circle of any radius with O as the centre.

(2) Join the diametre AB of the circle.

(3) Taking O as the centre and OB as the segment, draw an angle of measure 45° such that it intersects the circle at point C.

(Since we need ∠CAB =, we have drawn ∠COB = 45°.)

(4) Join AC.

∠CAB is the required angle.

(iii)

To construct the required angle at point A with one side along AB, we will use the following property.

Angle made by an arc at any point on the alternate arc is equal to half the angle made at the centre.

(1) Draw a circle of any radius with O as the centre.

(2) Take two points A and B on the upper side of the centre and join AB.

(3) Join OB.

(4) Taking O as the centre and OB as the segment, draw an angle of measure 45° such that it intersects the circle at point C.

(Since we need ∠CAB =, we have drawn ∠COB = 45°.)

(5) Join AC.

∠CAB is the required angle.