Question

Using a protractor, draw an angle of measure ${72}^{\circ }$. With this angle as given, draw angles of measure ${36}^{\circ }and{54}^{\circ }$.

Answer 1

Steps of construction :

(i) Draw an angle ABC = ${72}^{\circ }$ with the help of protractor.

(ii) With centre B and a suitable radius, draw an arc EF.

(iii) With centre E and F, draw arcs intersecting each other at G and produce it to D.

Then BD is the bisector of $\angle$ABC.

$\therefore \angle DBC={72}^{\circ }\times \frac{1}{2}={36}^{\circ }$.

(iv) Again bisect $\angle$ABD in the same way then PB is the bisector of $\angle$ABD.

$\therefore \angle PBC={36}^{\circ }+\frac{1}{2}\times {36}^{\circ }$

$={36}^{\circ }+{18}^{\circ }={54}^{\circ }$

Hence $\angle PBC={54}^{\circ }$