Question

Using ruler and compasses, construct the following angles
(i) 75${}^o$
(ii) 180${}^o$

Answer 1

(i) ${75}^o$
Steps of Construction:
Step 1 : Construct a line segment BC.
Step 2:Taking B as the centre and suitable radius, construct an arc and cut off PQ then QR of the same radius
Step3:Taking Q and R as centres, construct two arcs which intersect each other at the point S.
Step 4: Now join SB.
Step 5:Taking Q and D as centres, construct two arcs which intersect each other at the point T.
Step 6: Now join BT and produce it to point A.
Thus, $\angle ABC={75}^0$


(ii) ${180}^o$
Steps of Construction:
Step 1: Construct a line segment BC.
Step 2: Taking B as the centre and some suitable radius, construct an arc which meets BC at the point P.
Step 3: Taking P as centre and with the same radius, cut off the arcs PQ, QR and RS.
Step 4: Now join BS and produce it to point A.
Thus, $\angle ABC={180}^o$