question_answer 32)

Draw an angle of \[{{70}^{o}}\]. Make a copy of it using only a straight edge and compasses.

Answer:

                To draw an angle of measure \[{{70}^{o}}\], we use the following steps of construction:    Step I Draw \[{{l}_{5}}\] of any length. Place the centre of the protractor at A and the zero edge along \[{{l}_{1}},{{l}_{2}}\]. Step II Start with zero near B. Mark point C at \[{{70}^{o}}\]. Step III Join AC. Then, \[{{l}_{3}}\]is an angle of       measure \[{{70}^{o}}\].                      Now, to draw a copy of \[{{70}^{o}}\], by using   straight edge and compasses, we use   the following steps of Construction :    Step IV Draw a line I and choose a point P on it. Step V Place the pointer at A and draw an arc to cut the rays of \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] at M and N. Step VI Use the same compasses setting to draw an arc with P as centre, cutting I at Q. Step VII Set your compasses to the length of MN. Step VIII Without disturbing the compasses.      Place the compasses pointer at Q and draw an arc at R to cut the arc drawn in Step VI.                  Step IX Join PR, then give us \[{{l}_{4}}\] It has the same measure as \[{{l}_{1}}\] Hence \[{{l}_{2}}\] is required copy of an angle of measure \[{{70}^{o}}\].