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1.Construct a line segment (PQ) of lenght 8.3cm using ruler and compasses.

2.Draw any line segment (AB).Mark a point P on it. Using ruler and compasses construct (PQ) such that (PQ) is perpendicular to (AB).

3.Draw (LM)=10cm. Using compasses and ruler divide (LM) into four equal parts.Measure each part and write the length.

4.Using compasses and ruler construct 105 (degree)

5.Construct a perpendicular bisector of (PQ), whose length is 11.2cm using compasses and ruler.

6.Draw an angle of measure 140 (degree) aand divide it into 4 equal parts using ruler and compasses.

**4).**

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°

**5).**

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.

**6).**

Hi,

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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