# Construct the following angles at the initial point of a given ray and justify the construction: (i) 45° (ii) 90°

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Construct the following angles at the initial point of a given ray and justify the construction: (i) 45° (ii) 90°

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(i) Steps of construction:

1. Draw a line segment AB and produce BA to point C.

2. With center A and any radius drawn an arc which intersect AC at D and AB at E.

3. With center D and E and radius more than DE/2 draw arcs cutting each other at F.

4. Join FA which intersect arc in (2) at G.

5. With centers G and E and radius more than GE/2 draw arcs cutting each other at H.

6. Join HA

Therefore ∠HAB = 45o

(ii) Steps of construction:

1. Draw a line segment AB.

2. With center A and any radius draw in arc which intersect AB at C.

3. With center C and same radius draw an arc which intersects previous arc at D.

4. With centers D same radius draw an arc which intersects are in (2) at E.

5. With centers E and D same radius more than ED/2 draw an arc cutting each other at F.

6. Join FA

Therefore ∠FAB = 90o