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Question
In the adjacent figure HOPE is a parallelogram. Find the angle measures x,y and z. State the geometrical truths you use to find them.
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Solution
\[\angle HOP + 70°= 180° (\text{ linear pair })\]
\[\angle HOP = 180°- 70°= 110°\]
\[x = \angle HOP = 110° (\text{ opposite angles of a parallelogram are equal })\]
\[\angle EHP + \angle HEP = 180°(\text{ sum of adjacent angles of a parallelogram is } 180°)\]
\[110° + 40° + z = 180°\]
\[z = 180° - 150°= 30°\]
\[y = 40° \left( \text{ alternate angles }\right)\]
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