Question

(a) Draw an angle of measure ${115}^{\circ }$ and construct its bisector.
(b) Suppose an angle (whose measure we do not know) is given and you have to make a copy of this angle. How will you do it? [4 MARKS]

Answer 1

(a) Construction: 1 Mark
Steps: 1 Mark
(b) Construction: 1 Mark
Steps: 1 Mark


(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 compasses.
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 compasses at A and draw an arc to cut the rays of $\angle A$ at B and C.




Step 3: Use the same compasses setting to draw an arc with P as centre, cutting l in Q



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



Step 5: Place the compasses 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 $\angle BAC$