Question

Construct $∆$PQR such that $\angle$Q = 70$°$, $\angle$R = 80$°$ and PQ + QR + PR = 10 cm.

Answer 1

Steps of construction:
1. Draw DA = 10 cm.
2. Draw rays DY and AX, such that $\angle \mathrm{ADY}=35°\mathrm{and}\angle \mathrm{DAX}=40°$. The rays DY and AX intersect at P.
3. Draw the perpendicular bisector of seg DP, intersecting seg DA at point Q.
4. Draw the perpendicular bisector of seg AP, intersecting seg DA at point R.
5. Join P-Q and P-R.
7. Hence, $△$PQR is the required triangle.