Construct with rulerand compasses, angles of following measures:
(a) 60° (b) 30° (c) 90°
(d) 120° (e) 45° (f) 135°
Construct with rulerand compasses, angles of following measures:
(a) 60° (b) 30° (c) 90°
(d) 120° (e) 45° (f) 135°
(a) 60°
Thebelow given steps will be followed to construct an angle of 60°.
(1) Draw a line l and mark a point P on it. Now, taking P ascentre and with a convenient radius, draw an arc of a circle whichintersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at point R.
(3) Join PR which is the required ray making 60°with line l.
(b) 30°
Thebelow given steps will be followed to construct an angle of 30°.
(1) Draw a line l and mark a point P on it. Now taking P ascentre and with convenient radius, draw an arc of a circle whichintersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at point R.
(3) Now, taking Q and R as centre and with radius more than 
RQ,draw arcs to intersect each other at S. Join PS which is the requiredray making 30° with line l.
(c) 90º
Thebelow given steps will be followed to construct an angle of 90°.
(1) Draw a line l and mark a point P on it. Now taking P ascentre and with a convenient radius, draw an arc of a circle whichintersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw anarc intersecting the arc at S (see figure).
(4) Taking R and S as centre, draw an arc of same radius to intersecteach other at T.
(5) JoinPT, which is the required ray making 90°with line l.
(d) 120º
Thebelow given steps will be followed to construct an angle of 120°.
(1) Draw a line l and mark a point P on it. Now taking P ascentre and with a convenient radius, draw an arc of a circle whichintersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw anarc intersecting the arc at S (see figure).
(4) JoinPS, which is the required ray making 120°with line l.
(e)45º
Thebelow given steps will be followed to construct an angle of 45°.
(1) Draw a line l and mark a point P on it. Now taking P ascentre and with a convenient radius, draw an arc of a circle whichintersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw anarc intersecting the arc at S (see figure).
(4) Taking R and S as centres, draw arcs of same radius to intersecteach other at T.
(5) Join PT. Let it intersect the major arc at point U.
(6) Taking Q and U as centres, draw arcs with radius more than QUto intersect each other at V. Join PV.
PV isthe required ray making 45°with the given line l.
(f) 135°
Thebelow given steps will be followed to construct an angle of 135°.
(1) Draw a line l and mark a point P on it. Now taking P ascentre and with a convenient radius, draw a semi-circle whichintersects line l at Q and R.
(2) Taking R as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at S.
(3) Taking S as centre and with the same radius as before, draw anarc intersecting the arc at T (see figure).
(4) Taking S and T as centre, draw arcs of same radius to intersecteach other at U.
(5) Join PU. Let it intersect the arc at V. Now taking Q and V ascentres and with radius more than QV,draw arcs to intersect each other at W.
(6) JoinPW which is the required ray making 135°with line l.
(a) 60°
Thebelow given steps will be followed to construct an angle of 60°.
(1) Draw a line l and mark a point P on it. Now, taking P ascentre and with a convenient radius, draw an arc of a circle whichintersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at point R.
(3) Join PR which is the required ray making 60°with line l.
(b) 30°
Thebelow given steps will be followed to construct an angle of 30°.
(1) Draw a line l and mark a point P on it. Now taking P ascentre and with convenient radius, draw an arc of a circle whichintersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at point R.
(3) Now, taking Q and R as centre and with radius more than RQ,draw arcs to intersect each other at S. Join PS which is the requiredray making 30° with line l.
(c) 90º
Thebelow given steps will be followed to construct an angle of 90°.
(1) Draw a line l and mark a point P on it. Now taking P ascentre and with a convenient radius, draw an arc of a circle whichintersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw anarc intersecting the arc at S (see figure).
(4) Taking R and S as centre, draw an arc of same radius to intersecteach other at T.
(5) JoinPT, which is the required ray making 90°with line l.
(d) 120º
Thebelow given steps will be followed to construct an angle of 120°.
(1) Draw a line l and mark a point P on it. Now taking P ascentre and with a convenient radius, draw an arc of a circle whichintersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw anarc intersecting the arc at S (see figure).
(4) JoinPS, which is the required ray making 120°with line l.
(e)45º
Thebelow given steps will be followed to construct an angle of 45°.
(1) Draw a line l and mark a point P on it. Now taking P ascentre and with a convenient radius, draw an arc of a circle whichintersects line l at Q.
(2) Taking Q as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at R.
(3) Taking R as centre and with the same radius as before, draw anarc intersecting the arc at S (see figure).
(4) Taking R and S as centres, draw arcs of same radius to intersecteach other at T.
(5) Join PT. Let it intersect the major arc at point U.
(6) Taking Q and U as centres, draw arcs with radius more than QUto intersect each other at V. Join PV.
PV isthe required ray making 45°with the given line l.
(f) 135°
Thebelow given steps will be followed to construct an angle of 135°.
(1) Draw a line l and mark a point P on it. Now taking P ascentre and with a convenient radius, draw a semi-circle whichintersects line l at Q and R.
(2) Taking R as centre and with the same radius as before, draw anarc intersecting the previously drawn arc at S.
(3) Taking S as centre and with the same radius as before, draw anarc intersecting the arc at T (see figure).
(4) Taking S and T as centre, draw arcs of same radius to intersecteach other at U.
(5) Join PU. Let it intersect the arc at V. Now taking Q and V ascentres and with radius more than QV,draw arcs to intersect each other at W.
(6) JoinPW which is the required ray making 135°with line l.
