Question

Using your protractor, draw an angle of measure ${108}^{\circ }$. With this angle as given, draw an angle of ${54}^{\circ }$.

Answer 1

Steps of construction :

(i) With the hlep of protractor draw an angle ABC = ${108}^{\circ }$.

As ${54}^{\circ }=\frac{1}{2}\times {108}^{\circ }$

$\therefore$ We shall bisect it.

(ii) With centre B and suitable radius, draw an arc meeting BC at E and AB at F.

(iii) With centre E and F, and radius more than half of EF, draw arcs intersecting each other at G.

(iv) Join BG and produce it to D.

Then $\angle$DBC = ${54}^{\circ }$.