(a) 2 Marks     
(b) 2 Marks 
(a) The steps given below should be followed to construct an angle and its bisector:
i) Draw a line l and mark a point 'O' on it.
ii) Mark a point A at ${115}^{\circ }$ with the help of protractor. Join OA.
iii) Draw an arc of convenient radius, while taking point O as the centre. Let it intersect both rays of the ${115}^{\circ }$ angle at point A and B.
iv) Taking A and B as centres, draw an arc of radius more than $\frac{1}{2}$  AB in the interior of the angle of ${115}^{\circ }$. Let those intersect each other at C. Join OC.
OC is the required bisector of the angle of ${115}^{\circ }$. 

(b) As usual, we will have to use only a straight edge and the compass.  
     Given $\angle A$, whose measure is not known.

Step 1: Draw a line l and choose a point P on it.
             
Step 2: Place the compass at A and draw an arc to cut the rays of $\angle A$ at B and C.

Step 3: Use the same compass setting to draw an arc with P as centre, cutting l in Q
    
Step 4: Set your compass to the length BC with the same radius.
 
   
Step 5: Place the compass pointer at Q and draw the arc to cut the arc drawn earlier in R.
           
Step 6: Join PR. This gives us $\angle P$. It has the same measure as $\angle A$.
         
  This means  $\angle QPR$ has the same measure as $\angle BAC$.