Question

Construct with ruler and compasses, angles of following measures:

(a) 60° (b) 30° (c) 90°

(d) 120° (e) 45° (f) 135°

Answer 1

(a) 60°

The below 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 as centre and with a convenient radius, draw an arc of a circle which intersects line l at Q.

(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point R.

(3) Join PR which is the required ray making 60° with line l.

(b) 30°

The below 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 as centre and with convenient radius, draw an arc of a circle which intersects line l at Q.

(2) Taking Q as centre and with the same radius as before, draw an arc 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 required ray making 30° with line l.

(c) 90º

The below 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 as centre and with a convenient radius, draw an arc of a circle which intersects line l at Q.

(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at R.

(3) Taking R as centre and with the same radius as before, draw an arc intersecting the arc at S (see figure).

(4) Taking R and S as centre, draw an arc of same radius to intersect each other at T.

(5) Join PT, which is the required ray making 90° with line l.

(d) 120º

The below 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 as centre and with a convenient radius, draw an arc of a circle which intersects line l at Q.

(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at R.

(3) Taking R as centre and with the same radius as before, draw an arc intersecting the arc at S (see figure).

(4) Join PS, which is the required ray making 120° with line l.

(e)45º

The below 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 as centre and with a convenient radius, draw an arc of a circle which intersects line l at Q.

(2) Taking Q as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at R.

(3) Taking R as centre and with the same radius as before, draw an arc intersecting the arc at S (see figure).

(4) Taking R and S as centres, draw arcs of same radius to intersect each 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 QU to intersect each other at V. Join PV.

PV is the required ray making 45° with the given line l.

(f) 135°

The below 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 as centre and with a convenient radius, draw a semi-circle which intersects line l at Q and R.

(2) Taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S.

(3) Taking S as centre and with the same radius as before, draw an arc intersecting the arc at T (see figure).

(4) Taking S and T as centre, draw arcs of same radius to intersect each other at U.

(5) Join PU. Let it intersect the arc at V. Now taking Q and V as centres and with radius more than QV, draw arcs to intersect each other at W.

(6) Join PW which is the required ray making 135° with line l.