Given below ar the angles x and y.
Without measuring these angles, construct :
(i)∠ABC=x+y(ii)∠ABC=2x+y(iii)∠ABC=x+2y
Given below ar the angles x and y.
Without measuring these angles, construct :
(i)∠ABC=x+y(ii)∠ABC=2x+y(iii)∠ABC=x+2y
(i) Steps of Construction :
1. Draw a line segment BC of any suitable length.
2. With B as 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 produce upto point A. Thus \angle 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 upto 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.
Join BG and produce it upto 'A'. Thus ∠ABC = x + y + y = x + 2y
(i) Steps of Construction :
1. Draw a line segment BC of any suitable length.
2. With B as 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 produce upto point A. Thus \angle 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 upto 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.
Join BG and produce it upto 'A'. Thus ∠ABC = x + y + y = x + 2y
