Ex 3.3, 7 The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them. Given,
a Parallelogram HOPE where
∠EHP = 40° and ∠POX = 70°
Now,
HOX is a line Segment,
∠ HOP + ∠POX = 180°
∠ HOP + 70° = 180°
∠ HOP = 180° − 70°
∠ HOP = 110°
We know that
Opposite angles of a Parallelogram are equal
∠E = ∠HOP
x = 110°
Also,
Adjacent angles of a Parallelogram are Supplementary
∠EHO + ∠HOP= 180°
40° + z + 110° = 180°
150° + z = 180°
z = 180° − 150°
z = 30°
In ∆ PHO,
Sum of angles
∠ PHO + ∠HPO + ∠POH = 180°
z + y + 110° = 180°
30° + y + 110° = 180°
y + 140° = 180°
y = 40°
Therefore,
x = 110° , y = 40° and z = 30°

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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