question_answer 31)

Draw an angle of measure \[{{135}^{o}}\] and bisect it.

Answer:

                Here, to bisect an angle of \[{{135}^{o}}\], we use the following steps of construction: Step I Draw \[{{l}_{4}}\] of any length. Place the centre of the protractor at A and the zero edge along \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]. Step II   Start with zero near A. Mark point C at \[{{135}^{o}}\]. Step III Join AC. Then, \[{{l}_{4}}\]is an angle of measure \[{{135}^{o}}\]. Step IV With A as centre and using compasses, draw an arc that cuts both sides of\[{{l}_{1}}\]  at points P and Q. Step V  With P as centre, draw (in the interior of \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\]) an arc, whose radius is more than half of length PQ. Step VI With the same radius and with Q as centre, draw another arc in the interior of \[{{l}_{6}}\]. Let the two arcs intersect at D. Join \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] Then, \[{{l}_{6}}\]is the required bisector of i.e. \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}}\]