2. If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
7. In Fig. 13.34, ABCD is a parallelogram in which ZDAB = 75° and ZDBC = 61%
13.20
parallelogram
3. Find the measure of all the angles of a parallelogram, if one
twice the smallest angle.
the measure of the shorter side?
5. In a parallelogram ABCD, ZD = 135°, determine the measures of ZA and <B
6. ABCD is a parallelogram in which ZA = 70°. Compute ZB, ZC and <D.
Compute ZCDB and ZADB.
D
"The perimeter of a pparallelogrem is 22 cm. If the longer side measures 6.5 cm wka
,
60°
75°
А
B
Fig. 13.34
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Answer:
Explanation:
Let in a parallelogram
A
B
C
D
,
∠
A
=
x
Then its adjacent angle ,
∠
B
=
2
3
x
But,
∠
A
+
∠
B
=
180
∘
[Since, sum of the consecutive angles of a parallelogram is
180
∘
.
⇒
x
+
2
3
x
=
180
∘
⇒
3
x
+
2
x
3
=
180
∘
⇒
5
x
3
=
180
∘
⇒
x
=
180
∘
×
3
5
⇒
x
=
36
∘
×
3
⇒
x
=
108
∘
⇒
∠
A
=
108
∘
---(1)
⇒
∠
B
=
180
∘
−
108
∘
=
72
∘
---(2)
Since, opposite angles of a parallelogram are equal.
⇒
∠
A
=
∠
C
=
108
∘
---(3)
and
⇒
∠
B
=
∠
D
=
72
∘
---(4)
Hence angles are
108
∘
,
72
∘
,
108
∘
,
72
∘
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