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Byju's Answer
Standard IX
Mathematics
Postulate5
In figure, if...
Question
In figure, if AB ∥ CD, CD ∥ EF and y : z = 3 : 7, then find x.
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Solution
Given CD || EF
⇒
∠
C
G
H
=
∠
F
H
G
(
∵
Alternate interior angles are equal)
⇒
∠
C
G
H
=
z
Also,
∠
C
G
I
+
∠
C
G
H
=
180
∘
(
∵
They both form a linear pair)
⇒
y
+
z
=
180
∘
(i)
Given y : z = 3 : 7
Let us consider y as 3k and z as 7k.
y
+
z
=
180
∘
(from (i))
⇒
3
k
+
7
k
=
180
∘
⇒
10
k
=
180
∘
⇒
k
=
18
∘
⇒
z
=
7
k
=
7
(
18
∘
)
=
126
∘
Also, AB || CD
x
=
z
(
∵
Corresponding angles are equal)
⇒
x
=
126
∘
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