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.

 

Answer 1

\[\angle HOP + 70°= 180° (\text{ linear pair })\]
\[\angle HOP = 180°- 70°= 110°\]
\[x = \angle HOP = 110° (\text{ opposite angles of a parallelogram are equal })\]
\[\angle EHP + \angle HEP = 180°(\text{ sum of adjacent angles of a parallelogram is } 180°)\]
\[110° + 40° + z = 180°\]
\[z = 180° - 150°= 30°\]
\[y = 40° \left( \text{ alternate angles }\right)\]