Question

in rhombus pqrs diagonals pr and qs meet each other at o, if angle prq = 50 find angle psq

Answer 1

$$\begin{gathered} \mathrm{As}\mathrm{we}\mathrm{know}\mathrm{that}\mathrm{diagonal}\mathrm{of}\mathrm{a}\mathrm{rhombus}\mathrm{bisects}\mathrm{the}\mathrm{angle}\mathrm{so}, \\ \angle \mathrm{SRQ}=2\angle \mathrm{PRQ}=100 \\ \mathrm{Now}\mathrm{angle}\angle \mathrm{SRQ}\mathrm{and}\angle \mathrm{PSR}\mathrm{are}\mathrm{linear}\mathrm{pair}\mathrm{so} \\ \angle \mathrm{SRQ}+\angle \mathrm{PSR}=180 \\ \angle \mathrm{PSR}=80 \\ \mathrm{Now}\mathrm{angle}\mathrm{PSQ}=\frac{1}{2}\angle \mathrm{PSR}=40 \end{gathered}$$