Question

Using ruler and compasses only, construct a triangle ABC having $\angle C={135}^{\circ }$ and $\angle B={30}^{\circ }$. BC = 5 em. Bisect angles B and C and measure the distance of A from the paint where the bisectors meet.

Answer 1

Steps : (i) Draw $BC=5cm$
(ii) Draw $AC$ such that $\angle C={135}^o$.
(iii) Draw $AB$ such that $\angle ABC={30}^o$.so that both meet at A.Thus
$ABC$ is the required triangle
(iv) Draw bisectors of $\angle B$ and $\angle C$ so that both meet at P.
(v) Join AP and measure it. Hence, $AP=9.4cm$