Question

Construct $∆$XYZ whose perimeter is 12 cm and $\angle$Y = 70$°$ and $\angle$Z = 80$°$.

Answer 1

Steps of construction:
1. Draw DA = 12 cm.
2. Draw rays DQ and AP, such that $\angle \mathrm{ADQ}=35°\mathrm{and}\angle \mathrm{DAP}=40°$. The rays DQ and AP intersect at X.
3. Draw the perpendicular bisector of seg DX, intersecting seg DA at point Y.
4. Draw the perpendicular bisector of seg AX, intersecting seg DA at point Z.
5. Join XY and XZ.
7. Hence, $△$XYZ is the required triangle.