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Chord AB and CD when produced …

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Chord AB and CD when produced meet outside the circle at E. If angle EAD=35° angle AED=40°,find angle CBE.

Posted by Sadhna Kashyap 8 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Naveen Sharma 8 years, 10 months ago

Ans.

\(GIven : \space \angle EAD = 35 \) \(and \space \angle AED = 40\)

\(To \space Find : \space \angle CBE \)

\(Proof : \space in \space \triangle EAD \)

=> \(\angle AED + \angle EAD + \angle ADE = 180 \space [angle \space sum \space property ]\)

=> \(\angle ADE = 180 -(35 +40) = 105 \)

=> \( \angle ADE + \angle ADC =180 \space [Linear \space Pair]\)

=> \(\angle ADC = 180 - 105 = 75 \)

\(Now \space \angle ADC = \angle ABC [angle\space made\space by\space same\space arc\space AC ]\)

=> \(\angle ABC = 75 \)

=> \( \angle ABC + \angle CBE =180 \space [Linear \space Pair]\)

=> \(\angle CBE = 180 - 75 = 105 \)

1Thank You

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