(i) O ABCD is a
Parallelogram, ABD = 30°
ADB = 40°
Find ADC and
ABC. Fill in the blanks:-
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Answer:
ADB+∠DBA+∠BAD=180
o
[ Sum of angles of triangle is 180
o
]
⇒ 40
o
+30
o
+∠BAD=180
o
⇒ 70
o
+∠BAD=180
o
⇒ ∠BAD=110
o
⇒ ∠BAD=∠DCB=110
o
[ Opposite angles of parallelogram are equal ]
⇒ ∠BAD+∠ADC=180
o
[ Adjacent angles of parallelogram ]
⇒ ∠BAD+∠ADB+∠BDC=180
o
⇒ 110
o
+40
o
+∠BDC=180
o
⇒ ∠BDC=180
o
−150
o
⇒ ∠BDC=30
o
∴ ∠ADC=40
o
+30
o
=70
o
⇒ ∠ADC=∠ABC=70
o
[ Opposite angles of parallelogram are equal ]
∴ ∠BAD=110
o
,∠DCB=110
o
,∠ADC=70
o
and ∠ABC=70
o
∴∠BAD−∠DCB+∠ADC−∠ABC=100−100+70−70=0
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