Constrction Angles of Special Measures

1. Constructing a 60° Angle Using a Compass

Instead of using a protractor, we can construct a 60° angle using only a compass and ruler. Here’s how:

Steps of Construction:

Step 1: Draw a Base Line

• Draw a straight line l and mark a point O on it.

Step 2: Draw the First Arc

• Place the compass pointer at O and set a convenient radius.
• Draw an arc that intersects line l at a point A.

Step 3: Draw the Second Arc

• Without changing the compass width, place the compass pointer at A.

• Draw another arc that intersects the first arc at B.

Step 4: Draw the Angle

• Join O to B using a straight line.

• ∠BOA = 60°, as it is formed using the properties of an equilateral triangle.

And that’s it! ∠BOA = 60° is successfully constructed using just a compass and a ruler.

Construction of 120° Angle

A 120° angle is simply twice a 60° angle. Instead of using a protractor, we can construct it using a compass and ruler by following these steps:

Steps of Construction:

Step 1: Draw a Base Ray

• Draw a ray OA of any length, with O as the starting point.

Step 2: Draw the First Arc

• Place the compass pointer at O and set a convenient radius.

• Draw an arc that intersects OA at M.

Step 3: Draw the Second Arc (to get 60°)

• Without changing the compass width, place the compass pointer at M.

• Draw another arc that intersects the first arc at P.

• ∠AOP = 60° at this step.

Step 4: Draw the Third Arc (to get 120°)

• Without changing the compass width, place the compass pointer at P.

• Draw another arc that intersects the first arc at Q.

• Now, ∠AOQ = 120° (since 60° + 60° = 120°).

Step 5: Draw the Required Angle

• Join OQ to complete the 120° angle.