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

How many arcs are required to be drawn to construct  an angle of 600 ?

Right Option : B
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Explanation
Question : 2

To construct an angle of 600 as shown in the figure the very first step is :

Right Option : C
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Explanation
Question : 3

Arrange the following steps in a correct order to construct a 60 angle as shown in the figure:

Step 1: Taking P as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point R.

Step 2: Join OB which is the required ray making 600 with line OA.

Step 3: Draw a line segment OA.

Step 4: Now, taking O as centre and with a convenient radius, draw an arc of a circle which intersects line OA at P.

Right Option : C
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Explanation
 
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