# 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.

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