Question

In $△$PQR seg PQ ${\cong }^{}$seg QR and $\angle$P = 70$°$, then find the measures of remaining angles of $△$PQR.

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{PQR}, \\ \mathrm{seg}\mathrm{PQ}\cong \mathrm{seg}\mathrm{QR} \\ \angle \mathrm{P}=70° \\ \mathrm{Thus},\angle \mathrm{P}=\angle \mathrm{R}=70°[\because \mathrm{seg}\mathrm{PQ}\cong \mathrm{seg}\mathrm{QR}] \\ \angle \mathrm{P}+\angle \mathrm{R}+\angle \mathrm{Q}=180°(\text{a}\mathrm{ngle}\mathrm{sum}\mathrm{proeprty}) \\ \Rightarrow 70°+70°+\angle \mathrm{Q}=180° \\ \Rightarrow \angle \mathrm{Q}=40° \\ \mathrm{Therefore},\angle \mathrm{P}=\angle \mathrm{R}=70°\text{and}\angle \mathrm{Q}=40°. \end{gathered}$$