question_answer 1)

Draw an angle of measure \[{{45}^{o}}\] and bisect it.

Answer:

                Here we use the following steps of construction: Step I   Draw \[R\to \] of any length. Place the centre of the protractor at A and the zero edge along \[S\xrightarrow[{}]{{}}\]. Step II   Start with zero near B, mark point C at \[{{45}^{o}}\]. Step III Join AC. Then,\[{{l}_{1}}\] is an angle of measure \[{{45}^{o}}\]. Step IV Now, with A as centre and using compasses, draw an arc that cuts both rays of \[{{l}_{2}}\] at P and Q. Step V  With P as centre, draw (in the interior of \[{{l}_{2}},\]) 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 \[{{l}_{2}}\]. Let the two arcs intersect at D. Join \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] Then, \[{{l}_{4}}\] is the required bisector of \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]. i.e. angle bisector of angle \[{{45}^{o}}\].