Construct with ruler and compasses, angles of following measures:

(a) 60° (b) 30°

(c) 90° (d) 120°

(e) 45° (f) 135°

(a) Construction of 60.

Step 1: Draw a line AB using a ruler.

Step 2: Draw an arc of some radius using a compass. Using the same length cut another arc placing the compass on D as centre.

Step 3: Draw a line passing through this point to form AC. Measure angle CAB=60.

(b) Construction of 30.

Construct 60 using the above steps. Bisect the angle as follows:

Step 1: With D as centre draw an arc. With E as centre and same radius draw another arc.

Step 2: Draw a line through their point of intersection.

(c) Construction of 90.

Step 1: Draw a line AB using a ruler.

Step 2: Draw an arc of some radius using a compass. Using the same length cut another arc placing the compass on D as centre. Repeat with the previous arc.

Step 3: Draw an arc with D and E as centres to get the intersection. Draw a line through their point of intersection.

(d) Construction of 120.

Step 1: Draw a line AB using a ruler.

Step 2: Draw an arc of some radius using a compass. Using the same length cut another arc placing the compass on D as centre. Repeat with the previous arc. Draw a line through the point of intersection to get CA.

(e) Construction of 45.

Follow the steps in 5(c) to get 90. Bisect it to get 45.

(f) Construction of 135.

Step 1: Construct 90.

Step 2: Extend BA to T. With AD as radius draw an arc with centre N and cut AT at G.

Step 3: With G and N as centres draw 2 arcs. Join AM.