Question 8

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

Steps of construction:
(a) Draw an angle ${70}^{\circ }$ with protractor, i.e., $\angle POQ={70}^{\circ }$
(b) Draw a ray $\overline{AB}$.
(c) Place the compasses at O and draw an arc to cut the rays of $\angle POQ$ at L and M.
(d) Use the same compasses, setting to draw an arc with A as centre, cutting AB at X.
(e) Set your compasses setting to the length LM with the same radius.
(f) Place the compasses pointer at X and draw the arc to cut the arc drawn earlier at Y.
(g) Join AY.
Thus, $\angle YAX={70}^{\circ }$