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(i) O ABCD is aParallelogram, ABD = 30°ADB = 40°Find ADC and ABC. Fill in the blanks:- |
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Answer» 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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