question_answer 28)

Draw an angle of measure of \[{{153}^{o}}\] and divide it into four equal parts.

Answer:

                Here, to divide an angle of measure \[{{153}^{o}}\] into four equal parts, we use the following steps. Step I Draw \[M\to \]of any length. Place the centre of the protractor at A and the zero edge along \[E\to \]. Step II Start with zero near B. Mark point C at \[{{153}^{o}}\]. Step III Join AC, then \[T\to \]is an angle of measure \[{{153}^{o}}\]. Step IV With A as centre and using compasses, draw an arc that cuts both rays of \[R\to \] at P and Q. Step V   With P as centre, draw (in the interior of \[S\xrightarrow[{}]{{}}\]) an arc whose radius is more than half the length of PQ. Step VI With the same radius and with Q as centre, draw another arc in the interior of \[{{l}_{1}}\]. Let the two arcs intersect at O. Join \[{{l}_{2}}\]. Let \[{{l}_{2}},\] cut the arc PQ at J. Then, \[{{l}_{2}}\] divides the \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]in two equal parts. Step VII Now, with P and I as centre and with radius more than half of length PI, draw two arcs respectively, which cut each other at R. Step VIII Join \[{{l}_{4}}\] Then, \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] divides \[{{l}_{4}}\]into two equal parts. Step IX Now, with Q and I as centre and with radius more than half of length QI, draw two arcs respectively, which cut each other at M. Step X Join \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] Then, divide \[{{l}_{4}}\]into two equal parts. Thus, \[{{l}_{1}}\]and \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\]divide \[{{l}_{6}}\]into four equal parts.