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In figure (ii) given below, ABF is a straight line and BE || DC. If ∠DAB = 92° and ∠EBF = 20°, find

(i) ∠BCD

(ii) ∠ADC

In figure (ii) given below, ABF is a straight line and BE || DC. If ∠DAB = 92° and ∠EBF = 20°, find ∠BCD, ∠ADC. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Circles

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Answer

(i) Sum of opposite angles of cyclic quadrilateral = 180°

⇒ ∠DAB + ∠BCD = 180°
⇒ 92° + ∠BCD = 180°
⇒ ∠BCD = 180° - 92°
⇒ ∠BCD = 88°.

Hence, the value of ∠BCD = 88°.

(ii) ∠CBE = ∠BCD = 88° (∵ ∠CBE and ∠BCD are alternate angles)

∵ exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.

⇒ ∠ADC = ∠CBF
⇒ ∠ADC = ∠CBE + ∠EBF
⇒ ∠ADC = 88° + 20°
⇒ ∠ADC = 108°.

Hence, the value of ∠ADC = 108°.

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