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 the centre as B and a suitable radius, draw an arc to cut the rays BA and BC at F and E respectively.

(iii) With the centres as E and F, and with radius more than $\frac{1}{2}$EF, draw arcs intersecting each other at G. Join BG 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 $\angle PBC={54}^{\circ }$