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Question

Draw an angle of 80 using a protractor and divide it into four equal parts, using ruler and compass. Check your constuction by measurement.


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Solution

Here, to divide an angle of measure 80 into four equal parts, we use the following steps of construction:

Step I: Draw a line segment ¯¯¯¯¯¯¯¯AB of any length. Place the centre of the protractor at A and the zero edge along ¯¯¯¯¯¯¯¯AB

Step II: Start with zero near B and mark C at 80 .

Step III: Join AC, thenBAC is an angle of measure 80 .

Step IV: With A as centre and using compass, draw an arc that cuts both the rays of A at P and Q.

Step V: With P as centre, draw (in the interior of A an arc, whose radius is more than half the length of PQ.

Step VI: With Q as centre and the same radius, draw another arc in the interior of A Let the two arcs intersect at D. Join ¯¯¯¯¯¯¯¯¯AD Cutting are PQ at L then, AD divides the BCA into two equal parts.

Step VII :Now taking P and L as centre, having radius more than half of length PL, draw two arcs respectively, which cut each other at R

Step VIII: Join ¯¯¯¯¯¯¯¯AR which divides DAB into equal parts.

Step IX: Now taking Q and L as centre, having radius more than half of length QL draw two arcs respectively, which cut each other at M.

Step X: Join ¯¯¯¯¯¯¯¯¯¯AM, which divide CAD into two equal parts. Thus, ¯¯¯¯¯¯¯¯¯¯AM ¯¯¯¯¯¯¯¯¯ADand ¯¯¯¯¯¯¯¯AR divide BAC into four equal parts.


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