Question

In the figure abcd is a parrelogram find measure of angle adc measure of angle ecd and a measure of angle aec

Answer 1

Answer:

Here, ABCD is a parallelogram.

∠CBD=46

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[ Given ]

AD∥BC and AC is a transversal.

∴ ∠CBD=∠BDA [ Alternate angles ]

∴ ∠BDA=46

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.

So, ∠ODA=46

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In △ODA,

⇒ ∠ODA+∠OAD+AOD=180

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⇒ 46

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+∠OAD+68

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=180

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⇒ 114

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+∠OAD=180

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⇒ ∠OAD=66

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∴ ∠CAD=66

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⇒ ∠D+∠A=180

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[ Sum of adjacent sides are supplementary in parallelogram ]

⇒ (∠CDB+∠BDA)+(∠CAD+∠BAC)=180

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⇒ (30

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+46

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)+(66

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+∠BAC)=180

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⇒ 142

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+∠BAC=180

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⇒ ∠BAC=38

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⇒ ∠BAC=∠ACD [ Alternate angles ]

∴ ∠ACD=38

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Now,

⇒ ∠ADC=∠CDB+∠BDA=30

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+46

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=76

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∴ We get, ∠CAD=66

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,∠ACD=38

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and ∠ADC=76

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