question_answer 20)

                The adjacent figure HOPE is a parallelogram. Find the angle measures \[x,\,y\] and \[z\]. State the properties you use to find them.

Answer:

                \[x={{180}^{o}}-{{70}^{o}}={{110}^{o}}\] |Linear pair property and the opposite angles of a parallelogram are equal measure. \[y={{40}^{\text{o}}}\] \[{{40}^{o}}+z+x={{180}^{o}}\] |The adjacent angles in a parallelogram are supplementary \[\Rightarrow \]               \[{{40}^{o}}+z+{{110}^{o}}={{180}^{o}}\] \[\Rightarrow \]         \[z+{{150}^{o}}={{180}^{o}}\] \[\Rightarrow \]               \[z={{180}^{o}}-{{150}^{o}}\] \[\Rightarrow \]               \[z={{30}^{o}}\].