Q2 of 38 Page 19

Let’s draw 90o, 45o, 60o, 30o, 120o, 75o, 105o, 135o, 150o by scale and pencil compass.

We need to draw angles 90°, 45°, , 60°, 30°, 120°, 75°, 105°, 135° and 150°.


Materials Required: Sheet of papers, pencil, compass and a scale.


Steps of construction of 90°:


1. Draw a line OA of any length using a scale.



2. Place the point of a compass at vertex O and draw an arc or circle of any radius smaller than length of OA, cutting the line OA at Q.



3. Place the point of the compass at Q, draw an arc or circle of radius equals to the length of OQ, cutting the arc drawn in step 2 at R.



4. Now, taking R as center, place the point of the compass at R and draw an arc or circle of radius equals to the length of OQ. Cut the arc drawn in step 2 at S.



5. Now, take S as center and draw an arc of radius equals to the length of OQ, cutting the circle/arc drawn in step 4 at B.



6. Join OB.



Thus, the angle obtained ∠AOB = 90°.



Steps of construction of 45°:


1. We have already constructed 90° angle.



2. Now, taking O as centre again draw an arc or circle of any radius cutting OA at X and OB at Y.



3. Taking X as centre, place the point of compass at X and draw an arc or circle of radius OX.



4. Now, taking Y as centre, draw an arc with the same radius OX cutting the previous arc at Z.



5. Join OZ and extend the line to C.



Thus, the angle obtained ∠AOC = 45°.



Steps of construction of :


In order to construct , we can simplify it first.




1. We have already constructed 45°.



2. Now, taking O as centre again draw an arc or circle of any radius cutting OA at X’ and OC at Y’. We can rub out other lines in order to avoid confusion.



3. Taking X’ as centre, place the point of compass at X’ and draw an arc or circle of radius OX’.



4. Now, taking Y’ as centre, draw an arc with the same radius OX’ cutting the previous arc at Z’.



5. Join OZ’ and extend the line to D.



Thus, the angle obtained .



Steps of construction of 60°:


1. Draw a line OA of any radius using a scale.



2. Fix one end of a compass at point O, and draw an arc or circle of radius equals to approximately half of length OA, cutting the line OA at Q.



3. From the point Q, draw an arc or circle of same radius cutting the arc formed in step 2 at R.



4. Join OR and extend it to B.



Thus, we have got ∠AOB = 60°.



Steps of construction of 30°:


1. Draw a line OA of any radius using a scale.



2. Place one end of compass at point O, and draw an arc or circle of any radius convenient, cutting the line OA at Q.



3. Place the compass at point Q, and draw an arc or radius of the same radius cutting the previous arc at R.



4. Now, place the compass at point R, and draw an arc or circle of the same radius cutting the arc drawn in step 3 at S.



5. Join OS, and extend the line to B.



Thus, we have got ∠AOB = 30°.



Steps of construction of 120°:


1. Draw a line OA of any radius using a scale.



2. Place one end of compass at point O, and draw an arc or circle of any radius convenient, cutting the line OA at Q.



3. Place one end of compass at point Q, and draw an arc or circle of the same radius, cutting the previous arc at R.



4. Place one end of the compass at point R, and draw an arc or circle of the same radius cutting the previous arc at S.



5. Join OS, and also extend it to B.



Thus, we have got the ∠AOB = 60°.



Steps of construction of 75°:


1. Draw a line OA of any radius using a scale.



2. Place one end of compass at point O, and draw an arc or circle of any radius convenient, cutting the line OA at Q.



3. Place one end of compass at point Q, and draw an arc or circle of the same radius, cutting the previous arc at R.



4. Place one end of the compass at point R, and draw an arc or circle of the same radius cutting the previous arc at S.



5. Now, take S as centre and draw an arc or circle of same radius cutting the previous arc at C.



6. Join OC, and name the intersection with the arc drawn at step 1 as Z.



7. Now, set the compass at Z with a radius just more than half of ZR and draw an arc or radius.



8. With the same radius, place the compass at R and draw an arc or radius cutting the previous arc at Y.



9. Join OY, and extend the line to B.



Thus, we have got ∠AOB = 75°.



Steps of construction of 105°:


1. Draw a line OA of any radius using a scale.



2. Place one end of compass at point O, and draw an arc or circle of any radius convenient, cutting the line OA at Q.



3. Place one end of compass at point Q, and draw an arc or circle of the same radius, cutting the previous arc at R.



4. Place one end of the compass at point R, and draw an arc or circle of the same radius cutting the previous arc at S.



5. Now, take S as centre and draw an arc or circle of same radius cutting the previous arc at C.



6. Join OC, and name the intersection with the arc drawn at step 1 as Z.



7. Now, set the compass at Z with a radius just more than half of ZS and draw an arc or radius.



8. Now, with S as centre, draw an arc or circle with the same radius cutting the previous arc at Y.



9. Join OY, and then extend the line to B.



Thus, we have got ∠AOB = 105°.



Steps of construction of 135°:


1. Draw a line OA of any radius using a scale.



2. Place one end of compass at point O, and draw an arc or circle of any radius convenient, cutting the line OA at Q.



3. Place the compass at Q and draw an arc or circle of the same radius, cutting the arc drawn in step 2 at R.



4. Setting the compass at R, with the same radius draw an arc or circle cutting the previous arc at S.



5. Again, setting the compass at S, draw an arc or circle with the same radius cutting the previous arc at P and T. Also, join OT so that we get ∠AOT = 180°.



6. Also, join OP so that ∠AOP = 90° cutting the arc drawn in step 2 at Z.



7. Taking Z and T as centers, with the same radius draw an arc or circle cutting each other at intersection Y.



8. Join OY and extend the line to B.



Thus, we have got ∠AOB = 135°.



Steps of construction of 150°:


1. Draw a line OA of any radius using a scale.



2. Place one end of compass at point O, and draw an arc or circle of any radius convenient, cutting the line OA at Q.



3. Place the compass at Q and draw an arc or circle of the same radius, cutting the arc drawn in step 2 at R.



4. Setting the compass at R, with the same radius draw an arc or circle cutting the previous arc at S.



5. Again, setting the compass at S, draw an arc or circle with the same radius cutting the previous arc at P and T. Also, join OT so that we get ∠AOT = 180°.



6. Also, join OP so that ∠AOP = 90° cutting the arc drawn in step 2 at Z.



7. Taking T as center, with the same radius draw an arc or circle cutting the arc drawn in step 5 at Y such that, ∠POY = 60°.



8. Extend the line OY to B.



Thus, we have got ∠AOB = 150°.



More from this chapter

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i.


ii.


iii.


iv.


v.


vi.


1

i. Through activity, folding a square sheet of paper construct angles of 45o, 90o.

ii. Let’s draw a parallelogram, cutting the paper and folding the angles let’s see how the diagonals intersect with each other.


iii. Folding the paper, let’s verify the properties of diagonals, square, rectangle and rhombus.


iv. Let’s construct a rhombus by 4 setsquares.


v. Let’s draw 45o, 90o the angles of 30o, 45o, 60o, 90o, 105o and 120o using set square.


3

In quadrilateral PLAN opposite sides are equal in length i.e, PL = AN = 6 cm and PN = LA = 5cm. Let’s draw three types of quadrilateral PLAN, let’s see when it will be a rectangle.

 4

Let’s write that conditions required for to draw a fixed square.