Question

Construct an angle of 105⁰ using a compass. (3 Marks)

Answer 1

Steps:
1. Take a ray PQ. Draw an arc of some radius taking P as its centre, which intersects PQ at R.
2. Taking R as centre and with the same spread of compass, draw an arc intersecting the previously drawn arc at S.
(1 Mark)
3. Taking S as centre and keeping the spread of compass same, draw another arc intersecting the arc at T.
4. Taking S and T as centres, draw an arc of same radius to intersect each other at U.
(1 Mark)
5. Join PU. Let it intersect the arc at V. Taking T and V as centre, draw arcs with radius more than $\frac{1}{2}$ of TV.
6. Let these arcs intersect each other at W. Join PW which is the required ray making 105⁰ with the given ray PQ.


(1 Mark)