(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 theABC 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.

ThusRBC is the required angle of 135°

(v) 15°

We will follow the following algorithm for the construction

STEP1: Construct the angleABC 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