Question

Question 1

Draw $\angle POQ$ of measure ${75}^{\circ }$ and find its line of symmetry.

Answer 1

The line of symmetry is a line segment that is drawn in between a diagram in order to make the diagram equally divided in two. The line of symmetry divides a picture into two parts so that one forms a mirror image of the other.

Steps of construction:

(a) Draw a line l and mark a point O on it.
(b) Place the pointer of the compasses at O and draw an arc of any radius which intersects the line l at A.
(c) Taking the same radius, with centre A, cut the previous arc at B.

(d) Join OB, then $\angle BOA={60}^{\circ }$ .
(e) Taking the same radius, with centre B, cut the previous arc at C.
(f) Draw bisector of $\angle BOC$. The angle is of ${90}^{\circ }$. Mark it at D. Thus, $\angle DOA={90}^{\circ }$
(g) Draw $\overline{OP}$ as bisector of $\angle DOB.$ Thus, $\angle POA={75}^{\circ }$

Line of symmetry will be the line which divides ${75}^{\circ }$ into two equal parts i.e. ${37.5}^{\circ }$ each.