Answer:
:
(a)2Marks
(b)2Marks
(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 compassat A and draw an arc to cut the rays of $\angle A$ at B and C.

Step 3: Use the same compasssetting to drawan arc with P as centre, cutting l in Q

Step 4: Set your compassto the length BC with the same radius.

Step 5: Place the compasspointer 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 $\angle BAC$.