Construct the following angles at the initial point of a given ray and justify the construction.

45^o

Construction of angle of 45°

Steps of construction:

Step 1: Draw a ray OA.

Step 2: With its initial point O as center and any radius, draw an arc, cutting OA at B.

Step 3: With center B and same radius (as in step 2), cut the previous drawn arc at C.

Step 4: With C as center and the same radius, draw an arc cutting the arc drawn in step 2 cutting at D.

Step 5: With D and E as centers and any convenient radius (more than DE). Draw to two arcs intersecting at E.

Step 6: Join OE. Then ∠AOE = 90°

Step 7: Draw the bisector ‘OF’ of ∠AOE. Then, ∠AOF = 45°

Justification: -

By construction, ∠AOE = 90° and OF is the bisector of ∠AOE.

Therefore,

∠AOF = ∠AOE

=

= 45°