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Byju's Answer
Standard VIII
Mathematics
Parallelograms
ABCD is a par...
Question
ABCD is a parallelogram. Find the angles
x
,
y
and
z
in the given figure.
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Solution
Since, ABCD is a parallelogram
∴
∠ADC = ∠ABC
⇒
x
=
z
.
.
.
(
i
)
Now, in right triangle EBC, we have
∠BEC + ∠EBC + ∠ECB = 180°
⇒ 90° + x + 40° = 180°
⇒ x = 180° – 130° = 50°
From
(
i
)
,
x
=
z
=
50°
Now, in
△
F
C
D
, we have
∠CFD + ∠FDC + ∠FCD = 180°
[Angle sum property]
⇒ 90° + 50° + ∠FCD = 180°
⇒ 140° + ∠FCD = 180°
⇒ ∠FCD = 180° – 140° = 40°
Also, in parallelogram ABCD, we have
∠ADC + ∠DCB = 180°
⇒ 50° + (∠FCD +
y
+ 40°) = 180°
⇒ 50° + 40° +
y
+ 40° = 180°
⇒
y
=
180° – 130°
⇒
y
=
50°
∴
x
=
y
=
z
=
50°
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