Draw angle PQR of measures 135 degree and find its axis of symmetry ?
Answers
Construct with ruler and compasses, angles of following measures:
(1) 60 (2) 30 (3) 90 (4) 120 (5) 45 (6) 135
Answer:
Steps of construction:
(1)60∘
30
(i) Draw a ray OL¯¯¯¯¯¯¯.
(ii) Taking O as centre and convenient radius, mark an arc, which intersects OL¯¯¯¯¯¯¯ at P.
(iii) Taking P as centre and same radius, cut previous arc at Q.
(iv) Join OQ.
Thus, ∠MOL is required angle of 60 .
(2) 30∘
31
(i) Draw a ray OL¯¯¯¯¯¯¯.
(ii) Taking O as centre and convenient radius, mark an arc, which intersects OL¯¯¯¯¯¯¯ at P.
(iii) Taking P as centre and same radius, cut previous arc at Q.
(iv) Join OQ. Thus, ∠MOL is required angle of 60∘.
(v) Put the pointer on P and mark an arc.
(vi) Put the pointer on Q and with same radius, cut the previous arc at N.
Thus, ∠NOL is required angle of 30∘ .
(3) 90∘
32
(i) Draw a ray OL¯¯¯¯¯¯¯.
(ii) Taking O as centre and convenient radius, mark an arc, which intersects OL¯¯¯¯¯¯¯ at X.
(iii) Taking X as centre and same radius, cut previous arc at Y.
(iv) Taking Y as centre and same radius, draw another arc intersecting the same arc at Z.
(v) Taking Y and Z as centres and same radius, draw two arcs intersecting each other at S. (vi) Join OS and produce it to form a ray OM.
Thus, ∠MOL is required angle of 90∘ .
(4) 120∘
33
(i) Draw a ray OI¯¯¯¯¯¯.
(ii) Taking O as centre and convenient radius, mark an arc, which intersects OI¯¯¯¯¯¯ at P.
(iii) Taking P as centre and same radius, cut previous arc at Q.
(iv) Taking Q as centre and same radius cut the arc at S.
(v) Join OS.
Thus, ∠ IOL is required angle of 120∘.
(5) 45∘
34
(i) Draw a ray OI¯¯¯¯¯¯.
(ii) Taking O as centre and convenient radius, mark an arc, which intersects OI¯¯¯¯¯¯ at X.
(iii) Taking X as centre and same radius, cut previous arc at Y.
(iv) Taking Y as centre and same radius, draw another arc intersecting the same arc at Z.
(v) Taking Y and Z as centres and same radius, draw two arcs intersecting each other at S.
(vi) Join OS and produce it to form a ray OJ. Thus, ∠ JOI is required angle of 90∘ .
(vii) Draw the bisector of ∠JOI.
Thus, ∠MOI is required angle of 45∘ .
(6) 135∘
35
(i) Draw a line PQ and take a point O on it.
(ii) Taking O as centre and convenient radius, mark an arc, which intersects PQ at I and J.
(iii) Taking I and J as centres and radius more than half of IJ, draw two arcs intersecting each other at R.
(iv) Join OR. Thus, ∠QOR = ∠POQ = 90∘.
(v) Draw OL¯¯¯¯¯¯¯ the bisector of ∠POR.
Thus, ∠QOL is required angle of 135∘ .