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### Theory:

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: