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.
By following this procedure, we can get what is 105 degree angle.
First make the reference line.
Place the needle of the compass on the point O at which the angle to be made.
Draw an arc with simple semi circle by taking some radius such that it intersects the reference line at point D.
Now place the compass needle at the point D and draw arc on semicircle at point E without changing radius.
Again draw the arc on same semi circle at centre of point E by without changing radius that intersect the point F.
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.
Now change the radius in compass, and draw two arcs from point E and F such that they intersect each other at point (B).
Join the point O and B. This line gives 90 degree angle ie is angle BOA = 90 degree.
Let this line BO intersects semicircular arc at point G.
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.
Join the point O and C.
The line OC which makes an angle of 105 degree with the reference line OA.
Hence, ∠AOC = 105°
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.
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°,