Question

If the figure , chords AB and CD of circle when produced meet at p . If angle APD = 36° and angle BCD = 25° ,than find angle ADC.

Answer 1

$Given \: chords \:AB \:and \:CD \:of \:circle\\ when \:produced \:meet \:at \:P .$

$\angle {APD} = 36\degree , \: \angle {BCD} = 25\degree$

$\red { To \:find \: \angle {ADC} = ? }$

$Join \: A \: and \:C \:to \: D \:and \:B \\respectively .$

$i ) In \: \triangle BCP , \\</p><p>Exterior \angle {ABC} = \angle {BPC} + \angle {BCP }$

$\pink {Exterior \:angle \: at \: B \: is \:equal \:to }$

$\pink { (sum \:of \: interior \: opposite \: angles )}$

$\implies \angle {ABC} = 36\degree + 25 \degree\\= 61 \degree \: ---(1)$

$ii) Now , \angle {ADC} = \angle {ABC}$

$\pink { (Angles \:in \:same \:segment )}$

$\implies \angle {ADC} = 61 \:degree \: [ From \; (1) ]$

Therefore.,

$\red { \angle { ADC}} \green {= 61 \:degree}$

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Answer 2

Answer:

61  degree

Step-by-step explanation:

∠APD = 36°

∠BCD = 25°

∠ABC =∠ BCD +∠ APD

∠ABC = 180 - (36+25)

∠ABC = 61°

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