Question

An exterior angle of a parallelogram is 110 degree find all the angles of a parallelogram

Answer 1

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Answer 2

Answer:

70°, 70°, 110°, 110°

Step-by-step explanation:

Let ABCD is a parallelogram,

Such that,

After expanding the side DC through C to O,

⇒ m∠BCO = 110°,

∵ m∠BCD + m∠BCO = 180°

⇒ m∠BCD + 110° = 180°

⇒ m∠BCD = 70°

Since, in a parallelogram the opposite interior angles are equal,

That is,

m∠BCD = m∠BAD and m∠ADC = m∠ABC,

Also, sum of all interior angles of a quadrilateral is 360°,

⇒ m∠BCD + m∠BAD + m∠ADC + m∠ABC = 360°

70° + 70° + m∠ADC + m∠ADC  = 360°

140° + 2m∠ADC  = 360°

2m∠ADC = 220°

m∠ADC = 110°

⇒ m∠ABC= 110°