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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