Answer:
Here, to divide an angle of measure \[80{}^\circ \] into four equal parts, we use the following steps of construction Step I: Draw \[\overline{AB}\] of any length. Place the centre of the protractor at A and the zero edge along \[\overline{AB}\] Step II: Start with zero near B. Mark C at \[80{}^\circ \] Step III: Join AC, then \[\angle BAC\]is an angle of measure \[80{}^\circ \]. Step IV: With A as centre and using compasses, draw an arc that cuts both rays of \[\angle A\] at P and Q. Step V: With P as centre, draw (in the interior of \[\angle A\]) an arc whose radius is more than half the length of PQ. Step VI: With the same radius with Q as centre, draw another arc in the interior of \[\angle A\]. Let the two arcs intersect at D. Join \[\overline{AD}\], which cuts the arc PQ at I. Then, \[\overline{AD}\] divides the \[\angle BAC\] in two equal parts. Step VII: Now taking P and I as centre, having radius more than half of length I, draw two arcs respectively, which cut each other at R. Step VIII: Join \[\overline{AR}\], which divides \[\angle BAD\] into two equal parts. Step IX: Now taking Q and I as centre, having radius more than half of length QI, draw two arcs respectively, which cut each other at M. Step X: Join \[\overline{AM}\]. Then, divide \[\angle CAD\] into two equal parts. Thus \[\overline{AM},\overline{AD}\] and \[\overline{AR}\] divide \[\angle BAC\] into four equal parts.
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