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, then∠BAC 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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