Construction of 60 Degree Angle


 
 
Concept Explanation
 

Construction of 60 Degree Angle

CONSTRUCTION OF 60 DEGREE ANGLE:

In order to construct an angle of large 60^{circ} with the help of ruler and compasses only, we follow the following steps:

Steps of Construction

STEP I  Draw a ray OA.

STEP II  With centre O and any radius draw an arc PQ with the help of compasses, cutting the ray OA at P.

STEP III  With centre P and the same radius draw an arc cutting the arc PQ at R.
STEP IV  Join OR and produce it to obtain ray OB.
The angle large angle AOB so obtained is the angle of measure large 60^{circ}.

Justification : Now, let us see how this method gives us the required angle of large 60^{circ}.

Join PR. Now  In large Delta OPR, we have

          OP = OR = PR                            [PR is an arc equal to radius]

large Rightarrow ;;Delta OPR  is an equilateral triangle.

large Rightarrow ;;angle OPR=60^{circ}

large Rightarrow ;;angle AOB=60^{circ}

CONSTRUCTION OF AN ANGLE OF large 120^{circ}

In order to construct an angle of large 120^{circ} by using ruler and compasses only, we follow the following steps:

Steps of Construction

STEP I  Draw a ray OA.

STEP II  With O as centre and any convenient radius, draw an arc PQ cutting OA at P.

STEP III With P as centre and the same radius draw an arc, cutting the arc PQ at R. Then taking R as centre and the same radius draw an arc cutting the arc PQ at S.
STEP IV  Join OS and produce it to any point B.
            large angle AOB so obtained is the angle of measure large 120^{circ}
Sample Questions
(More Questions for each concept available in Login)
Question : 1

Arrange the following steps in a sequence manner to construct an angle of 60^0 :

Step 1. Take P as a center and with the radius of the same length mark an arc on the former arc at a point R.

Step 2. On a plane, sheet draw a line segment OA.

Step 3. Join points O to R and produce up to point B.

Step 4. Take O as a center, draw an arc with proper radius.

Right Option : C
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Explanation
Question : 2

Arrange the steps in a proper manner to construct an angle of 60 degree :

1. With P as the centre and same radius as in step II , draw another arc intersecting the previous arc at R.

2. Join OR and extend it to B.

3. Draw a ray OA.

4. With O as the centre and a suitable radius draw an arc intersecting OA at P.

Right Option : C
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Explanation
Question : 3

What type of angle is 60 degree ?

Right Option : A
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Explanation
 
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