Question

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

 

Answer 1

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