Construct the following angles at the initial point of a given ray and justify the construction:
(i) 45°
(ii) 90°
We have to construct of an angle 45° and 90°
(i)
(ii)
We will follow the following algorithm to construct the given angles
Steps of construction
STEP1: Draw a ray BC.
STEP2: With B as a centre, and taking convenient radius, draw an arc, intersecting the ray BC at point N.
STEP3: With N as a centre, and taking the same radius, draw an arc cutting the previous arc at M.
STEP4: With M as a centre, and the same radius, draw an arc cutting the arc drawn in STEP 2 at L.
STEP5: With M as a centre, and the same radius draw an arc.
STEP6: With L as a centre, and the same radius, draw an arc cutting the arc drawn in STEP 5 at A.
STEP7: Draw the ray BA.
ABC = 90°
STEP 8 Bisect the 
ABC. Let BP be the bisecting ray.
So
PBC = 45°