Question

Construct a triangle $ABC$ whose perimeter is $12.5cm$ and whose base angles are ${60}^{\circ }$ and ${75}^{\circ }$

Answer 1

Steps of construction
$1$. Draw a line segment and locate points $P,Q$ such that $PQ=12.5cm$.
$2$. Construct rays $\overrightarrow{PR}$ such that $\angle QPR={60}^{\circ }$ and $\overrightarrow{QS}$ such that $\angle PQS={75}^{\circ }$.
$3$. Draw the bisectors $PL$ and $QM$ of $\angle QPR$ and $\angle PQS$ respectively. Let these intersect at $A$.
$4$. Draw the perpendicular bisector of $AP$ and $AQ$ and let these intersect $PQ$ at $B$ and $C$ respectively.
$5$. Join $AB$ and $AC$.
Then $ABC$ is the required triangle.