Q. 195.0( 4 Votes )

# In a parallelogra

Answer :

∠*ABC* = ∠*ADC* = 30° [Measure of opposite angles is equal in a parallelogram]

∠*BDC* = 10°………….. given

∠BDA = 30° - 10° = 20°

∠DAB = 180° - 30° = 150°

∠*BCD* = ∠*DAB* = 150° [Measure of opposite angles is equal in a parallelogram]

∠*DBA =* ∠*BDC = 10°* [Alternate interior angles are equal]

In ΔDOC

∠*BDC +* ∠*ACD +* ∠*DOC = 180°* [Sum of all angles og a triangle is 180°]

10° *+* 70° *+* ∠*DOC = 180°*

∠*DOC = 180°- 80°*

∠*DOC = 100°*

∠*DOC =* ∠*AOB = 100°* [Vertically opposite angles are equal]

∠*DOC +* ∠*AOD = 180°* [Linear pair]

100° *+* ∠*AOD = 180°*

∠*AOD = 180°- 100°*

∠*AOD = 80°*

∠*AOD =* ∠*BOC = 80°* [Vertically opposite angles are equal]

∠*ABC +* ∠*BCD* = 180° [In a parallelogram sum of adjacent angles is 180°]

30° *+* ∠*ACB +* ∠*ACD* = 180°

30° *+* ∠*ACB +* 70° = 180°

∠*ACB* = 180° - 100°

∠*ACB* = 80°

∠*ACB* = ∠*ACB* = 80° [Alternate interior angles are equal]

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