Construct the angles of the following measurements:
(i) 30°
(ii) 75°
(iii) 105°
(iv) 135°
(v) 15°
(vi) 22
(i) 30°
We will construct as follows
STEP1: Construct the angle 
ABC of 60°
STEP2: Bisect the ABC. Let the ray BE being the angle bisector.
Thus 
EBC = 30°
(ii) 75°
We will follow the following steps to construct
STEP1: Construct the
ABC of the measure 90°.
STEP2: Using the same ray BC, construct 
EBC of the measure 60°
STEP3: Bisect 
ABE which is of measure 30°. The ray BD is the angle bisector.
Here, 
DBC is of the measure 75°
(iii) 105°
We will follow the following algorithm for the construction
STEP1: Construct the 
ABC of the measure 90°.
STEP2: Using the same ray BC, construct 
EBC of the measure 60°
STEP3: Bisect 
ABE which is of measure 30°. The ray BD is the angle bisector
So
Here, 
FBD is of the measure 105°
(iv) 135°
We will follow the following algorithm for the construction
STEP1: Draw a line PC and take a point B on it.
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.
STEP8: Bisect the 
ABP. Let BR be the bisecting ray.
Thus
RBC is the required angle of 135°
(v) 15°
We will follow the following algorithm for the construction
STEP1: Construct the angle
ABC of 60°
STEP2: Bisect the 
ABC. Let the ray BE, be the angle bisector.
Thus 
EBC = 30°
STEP3: Bisect the 
EBC. Let the ray BG be the angle bisector.
Thus 
GBC = 15°
(vi)22
We will follow the following algorithm for the 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°
STEP8: Bisect the 
ABC. Let BP be the bisecting ray.
So, 
PBC = 45°
STEP9: Bisect the 
PBC. Let BR be the bisecting ray.
So,
RBC =22