Construct the angles of the following measurements: from Mathem

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 Multiple Choice QuestionsLong Answer Type

1. Construct an angle of 90° at the initial point of a given ray and justify the construction.
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2. Construct an angle of 45° at the initial point of a given ray and justify the construction.
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3. Construct the angles of the following measurements:


30 degree
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4. Construct the angles of the following measurements:

22 1 half degree


22 1 half degree

Given : A rayOA
Required : To construct an angle of 22 1 half degree at 0.

Steps of Construction:

1. Taking O as centre and some radius, draw an arc of a circle, which intersects OA, say at a point B.
2. Taking B as centre and with the same radius as before, draw an arc intersecting the previously drawn arc, say at a point C.


Given : A rayOARequired : To construct an angle of  at 0.Steps of C

3. Taking C as centre and with the same radius as before, draw an arc intersecting the arc drawn in step 1, say at D.
4. Draw the ray OE passing through C. Then ∠EOA = 60°.
5. Draw the ray OF passing through D. Then ∠FOE = 60°.
6. Next, taking C and D as centres and with radius more than 1 half CD, draw arcs to intersect each other, say at G.
7. Draw the ray OG. This ray OG is the bisector of the angle FOE, i.e.,

angle FOG equals angle EOG equals 1 half angle FOE
space space space space space space space space space equals space 1 half left parenthesis 60 degree right parenthesis space equals space 30 degree
Thus comma space angle GOA equals angle GOE plus angle EOA
space space space space space space space space space space space space space space space space space space equals space 30 degree plus 60 degree equals 90 degree

8. Now, taking O as centre and any radius, draw an arc to intersect the rays OA and OG, say at H and I respectively.

9. Next, taking H and I as centres and with the radius more than 1 half HI, draw arcs to intersect each other, say at J.

10. Draw the ray OJ. This ray OJ is the bisector of the angle GOA.

straight i. straight e. comma space space angle GOJ equals angle AOJ equals 1 half angle GOA
space space space space space space space space space space space space space space space space space equals space 1 half left parenthesis 90 degree right parenthesis equals 45 degree

11. Now, taking O as centre and any radius, draw an arc to intersect the rays OA and OJ, say at K and L respectively.

12. Next, taking K and L as centres and with the radius more than 1 half KL, draw arcs to intersect each other, say at M.

13. Draw the ray OM. This ray OM is the bisector of the angle AOJ, i.e., ∠JOM = ∠AOM

equals 1 half angle AOJ equals 1 half left parenthesis 45 degree right parenthesis equals 22 1 half degree

 

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5. Construct the angles of the following measurements:

15°
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6.

Construct the following angles and verify by measuring them by a protractor:

75°

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7.

Construct the following angles and verify by measuring them by a protractor:

105°

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8.

Construct the following angles and verify by measuring them by a protractor:

135°

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 Multiple Choice QuestionsShort Answer Type

9.

Construct an equilateral triangle, given its side and justify the construction.

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10. Construct an equilateral triangle with one side 6 cm. 
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