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In this lesson, let us construct some special angles by without using the protractor.

**i) Construction of**\(60°\)

**angle**:

**Step 1**: First draw a straight line, and mark a point \(A\) on it.

**Step 2**: Take the point \(A\) as centre, draw an arc of convenient radius to the line to meet at a point \(B\).

**Step 3**: With the same radius, take \(B\) as centre, draw an arc to cut the previous arc at \(C\).

**Step 4**: Join \(AC\). Then \(∠BAC\) is the required angle with the measure \(60°\).

**ii) Construction of**\(135°\)

**angle**:

**Step 1**: First draw a straight line, and mark a point \(A\) on it.

**Step 2**: Take the point \(A\) as centre, draw an arc as below which meet at a point \(B\).

**Step 3**: Take radius, and draw an arc for \(60°\), as shown above. This cuts an arc at point \(C\).

**Step 4**: Now take \(C\) as centre, draw an arc to with the same radius, point it as \(D\). Here the point \(D\) gives the angles of \(120°\).

**Step 5**: With the same radius, draw an arc from the point \(D\) that cuts the \(E\) which gives the \(180°\).

**Step 6**: Finally, draw the angle bisector between the two points \(D\) \((120°)\) and \(E\) \((180)\). The angle bisector separates the two points \(D\) and \(E\) and gives the angle \(150°\). Now again find the angle bisector between \(150°\) and \(120°\), the resultant gives the required angle \(135°\).

The measure of \(135°\) angle, can be drawn in many ways, without using the protractor. Refer the below video for further information and clarification to construct the \(135°\) angle.

**Construct**\(135°\)

**degree using ruler and compass**: