3.
Construct the following angles using ruler and compasses. Write the steps of construction
each case.
(1 75°
(ii) 15°
(111.) 105°
Step by step
Answers
105 degree:
Step 1: First make the reference line.
Step 2: place the needle of the compass on the point O at which the angle to be made.
Step 3: Draw an arc with simple semi circle by taking some radius such that it intersects the reference line at point D.
Step 4: Now place the compass needle at the point D and draw arc on semicircle at point E without changing radius.
Step 5: Again draw the arc on same semi circle at centre of point E by without changing radius that intersect the point F.
Step 6: Now we get point D, E and F with centre at O. Point E and point F correspond to angle 60 degree and 120 degree respectively.
Step 7: Now change the radius in compass, and draw two arcs from point E and F such that they intersect each other at point (B).
Step 8: Join the point O and B. This line gives 90 degree angle ie is angle BOA = 90 degree.
Step 9: Let this line BO intersects semicircular arc at point G.
Step 10: From point G draw an arc and without changing the radius draw another arc from point F such that they intersect each other at point C.
Step 11: Join the point O and C.
Step 12: The line OC which makes an angle of 105 degree with the reference line OA.
∠COA = 105°
15 degree:
Steps of Construction:
(i) Draw a line segment BC.
(ii) With centre B and a suitable radius draw an arc meeting BC at P.
(iii) With centre P and with same radius cut off the arc at Q.
(iv) Taking P and Q as curves, draw two arcs intersecting each other at D nnd join BD.
(v) With centre P and R, draw two more arcs intersecting each other at S.
(vi) Join BS and produce it to A.
Then ∠ABC = 15°.
75degree
Step of Construction:
(i) Take a ray OA.
(ii) With O as centre and any convenient radius, draw an arc cutting OA at C.
(iii) With C as centre and the same radius, draw an cutting the first arc at M.
(iv) With M as centre and the same radius, cut off an arc cutting again the first arc at L.
(v) With L and M as centre and radius of more than half of LM, draw two arcs cutting each other at B, join OB which is making 90°.
(vi) Now with N and M as centres again draw two arcs cutting each other at P.
(vii) Join OP.
∠POA = 105°
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