Question

Construct a triangle $ABC$ whose perimeter $12cm$ and whose base angles are ${50}^{\circ }$ and ${80}^{\circ }$

Answer 1

1. Draw a line segment $PQ=AB+BC+CA=12cm$

2. Make $\angle LPQ={50}^0$ and $\angle MQP={80}^0$

3. Now bisect $\angle LPQ$ and $\angle MQP$ such that their bisection meet at A.

4. Draw perpendicular bisectors of $AP$ and $AQ$ as $XY$ and $ST$ intersecting $PQ$ at $B$ and $C$ respectively.

5. Join $AB$ and $AC$.