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Byju's Answer
Standard IX
Mathematics
Opposite Angles in a Parallelogram Are Equal
Given figure,...
Question
Given figure, HOPE is a parallelogram. Find the measure of the angles x, y and z.
A
30
∘
, 40
∘
and 60
∘
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B
110
∘
, 40
∘
and 30
∘
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C
90
∘
, 70
∘
and 80
∘
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D
80
∘
, 20
∘
and 60
∘
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Solution
The correct option is
B
110
∘
, 40
∘
and 30
∘
∠
H
O
P
+ 70
∘
= 180
∘
[linear pair]
⇒
∠
H
O
P
= 180
∘
− 70
∘
= 110°
∵
Opposite angles of a parallelogram are equal
∴
x =
∠
H
O
P
= 110
∘
∠
E
H
O
+
∠
H
E
P
= 180
∘
[Sum of adjacent angles of a parallelogram is 180
∘
]
⇒
z
∘
+ 40
∘
+ x
∘
= 180
∘
⇒
z
∘
+ 40
∘
+ 110
∘
= 180
∘
⇒
z
∘
= 180
∘
− 150
∘
= 30
∘
y
∘
=
∠
E
H
P
= 40
∘
[alternate angles]
∴
x
∘
= 110
∘
y
∘
= 40
∘
z
∘
= 30
∘
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Similar questions
Q.
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.