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Byju's Answer
Standard VIII
Mathematics
Diagonals of a Rhombus Bisect Each-Other at Right Angles
In the given ...
Question
In the given figure, ABCD is a parallelogram. Find the values of x and y.
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Solution
We know that the opposite angles of a parallelogram are equal.
So,
(
3
x
−
10
)
∘
=
(
x
+
80
)
∘
⇒
3
x
−
x
=
80
∘
+
10
∘
⇒
2
x
=
90
∘
⇒
x
=
45
∘
Also, the consecutive angles of a parallelogram are supplementary.
So,
∠
B
+
∠
C
=
180
∘
(
3
x
−
10
)
∘
+
(
y
+
25
)
∘
=
180
∘
(
3
×
45
∘
)
−
10
∘
+
y
+
25
∘
=
180
∘
135
∘
−
10
∘
+
y
+
25
∘
=
180
∘
⇒
125
∘
+
y
+
25
∘
=
180
∘
⇒
y
=
180
∘
–
125
∘
−
25
∘
⇒
y
=
30
∘
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Q.
In Figure 2, ABCD is a parallelogram. Find the values of x and y.