ABCD is a cyclic quadrilateral such that ∠B=5∠D and ∠C=3∠A, Find the measure of the each angle of the moo
moo
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Answer:
∠A+∠C=180
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[ Sum of angles in cyclic quadrilateral are supplementary ]
⇒ 2x+4
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+2y+10
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=180
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⇒ 2x+2y=166
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∴ x+y=83
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----- ( 1 )
Now, ∠B+∠D=180
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⇒ y+3
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+4x−5
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=180
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⇒ 4x+y=182
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---- ( 2 )
Subtracting equation ( 1 ) from equation ( 2 ) we get,
x=33
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Substituting value of x in equation ( 1 ) we get,
y=50
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.
⇒ ∠A=(2x+4)
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=(2×33+4)
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=70
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⇒ ∠B=(y+3)
2
=(50+3)
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=53
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⇒ ∠C=(2y+10)
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=(2×50+10)
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=110
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⇒ ∠D=(4x−5)
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=(4×33−5)
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=127
o
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