1.Using compasses and ruler construct 105 degree.
2.Construct a perpendicular bisector of PQ ehose length is 11.2cm using compasses and ruler.
3.Draw an angle of measure 140 degree and divide it into 4 equal parts using compasses and ruler.
SOLUTION 1)
By following this procedure, we can get what is 105 degree angle.
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.
Hence, ∠AOC = 105°
SOLUTION 2)
Follow the given steps to construct the perpendicular bisector of the line segment.
Step 1: Draw a line segment, PQ of length 11.2 cm using compass.
Step 2: With P as centre and radius more than half the length of PQ, draw two arcs on opposite side of PQ.
Step 3: With Q as centre and radius same as taken in step 2, draw two arcs intersecting the previous arcs in A and B.
Step 4: Join AB.
Thus, AB is the required perpendicular bisector of line PQ.
SOLUTION 3)
Using compass, it isn't possible to construct an angle of 140° and thus dividing it into 4 equal parts.
The angles which can be drawn easily by compass are multiples of 15° such as 15°, 30°, 45°, 60°, 90°, 105°, 135°,
150° etc.