If one angle of a parallelogram is 108°, what will be the measure of its adjacent angle?
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Answer:
Let
A
B
C
D
is a parallelogram. Let
∠
A
D
C
=
x
.
Therefore,
∠
D
C
B
=
2
x
−
36
∘
Now, we know that adjacent angles of a parallelogram are supplementary.
⇒
∠
A
D
C
+
∠
D
C
B
=
180
∘
⇒
x
+
2
x
−
36
∘
=
180
∘
⇒
3
x
=
216
∘
⇒
x
=
216
∘
3
=
72
∘
Hence,
∠
A
D
C
=
72
∘
and
∠
D
C
B
=
108
∘
Also, opposite angles of a parallelogram are equal ,therefore,
⇒
∠
A
B
C
=
∠
A
D
C
=
72
∘
and
∠
B
A
D
=
∠
D
C
B
=
108
∘
Thus, the four angles of the parallelogram are
108
∘
,
72
∘
,
108
∘
,
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