Question

Given below are the angles x and y.

Without measuring these angles, construct :

(i)

(ii)

(iii)

Answer 1

(i) Steps of Construction :

1. Draw a line segment BC of any suitable length.
2. With B as the centre, draw an arc of any suitable radius. With the same radius, draw arcs with the vertices of given angles as centres. Let these arcs cut arms of the arc x at points P and Q and arms of angle y at points R and S.
3. From the arc, with centre B, cut DE = PQ arc of x and EF = RS arc of y
4. Join BF and produce up to point A.
   Thus ∠ABC = x + y

(ii) Steps of Construction :

Proceed in exactly the same way as in part(i)
takes DE = PQ = arc of x.
EF = PQ = arc of x and FG = RS = arc of y.
Join BG and produce it up to A.
Thus ∠ABC = x + x+ y = 2x + y

(iii) Steps of Construction :

Proceed in exactly the same way as in (ii)
taking DE = PQ = arc of x. and EF = RS = arc of y and FG = RS = arc of y.
4. Join BF and produce up to point A.
Thus ∠ABC = x + y + y = x + 2y