Question

Construct the angles of the following measurements:
(ii) $22{\frac{1}{2}}^{\circ }$

Answer 1

(ii) $22{\frac{1}{2}}^{\circ }$
Steps to construct an angle of $22{\frac{1}{2}}^{\circ }$
Step 1: Draw a ray PQ and draw an arc of some radius, taking point P as its centre, which intersects PQ at R.
Step 2: Taking R as the centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S.
Step 3: Taking S as the centre and with the same radius as before, draw an arc intersecting the arc at T ( see figure).
Step 4: Taking S and T as the centre, draw an arc of the same radius to intersect each other at U.
Step 5: Join PU, let it intersect the arc at point V.
Step 6: From R and V, draw arcs with radius more than $\frac{1}{2}RV$, to intersect each other at W and join PW.
Step 7: Let the ray PW intersect the arc at X. Taking X and R as the centre, with a radius more than $\frac{1}{2}RX$, draw arcs to intersect each other at Y.
Step 8: Joint PY which is the required ray that makes an angle of $22{\frac{1}{2}}^{\circ }$ with the ray PQ.