Question

Given below are the angles x, y, and z.

Without measuring these angles construct :

(i) (ii) (iii)

Answer 1

(i) Steps of Construction :

1. Draw line segment BC of any suitable length.

1. With B as a 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 angle x at the points P and Q and arms of the angle y at points R and S and arms of the angle z at the points L and M.
2. From the arc, with centre B, cut
   DE = PQ = arc of x, EF = RS = arc of y and FG = LM = arc of z.
3. Join BG and produce it up to A.
   Then ∠ABC = x + y + z

(ii) Proceed as in part (i) up to step 2.
3. From the arc, with centre B, cut

DE = 2PQ = 2 arc of x
EF = RS = arc of y
FG = LM = arc of z
4. Join BG and produce it up to point A
Then ∠ABC = 2x + y + z

(iii) proceed as in (i) up to step 2

3. Here cut arc DE = arc PQ = arc of x arc EF = 2 arc RS = 2 arc of y arc FG = arc LM = arc of z.
4. Join BG and produce it up to A
5. Then ∠ABC = x + 2y + z