Question

draw a cyclic quadrilateral and find the measure of each angle

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Answer 1

In given figure ABCD is a cyclic quadrilateral.

We know that, sum of the opposite angles in a cyclic quadrilateral is 180

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So, ∠BCD + ∠BAD = 180

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⇒ 125

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+ ∠BAD = 180

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⇒ ∠BAD = 180

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- 125

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∴ ∠BAD = 55

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---- (1)

Since, ∠ABD is an angle in semi-circle.

∴ ∠ABD = 90

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--- (2)

In △ABD,

∠ADB + ∠ABD + ∠BAD = 180

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∠ADB + 90

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+ 55

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= 180

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(From 1 and 2)

∴ ∠ADB = 35

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