Question

In the following figure RISK and CLUE are parallelograms. Find the measure of x.

Answer 1

$$\begin{gathered} \mathrm{In}\mathrm{the}\mathrm{parallelogram}\mathrm{RISK}: \\ \angle \mathrm{ISK}+\angle \mathrm{RKS}=180°(\mathrm{sum}\mathrm{of}\mathrm{adjacent}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{is}180°) \\ \angle \mathrm{ISK}=180°-120°=60° \\ \mathrm{Similarly},\mathrm{in}\mathrm{parallelogram}\mathrm{CLUE}: \\ \angle \mathrm{CEU}=\angle \mathrm{CLU}=70°(\mathrm{opposite}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{are}\mathrm{equal}) \\ \mathrm{In}\mathrm{the}\mathrm{triangle}: \\ x+\angle \mathrm{ISK}+\angle \mathrm{CEU}=180° \\ x=180°-\left(70°+60°\right) \\ x=180°-\left(70°+60°\right)=50° \end{gathered}$$