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In the Figure, Given Below, Find: (I) ∠Bcd, (Ii) ∠Adc, (Iii) ∠Abc, Show Steps of Your Working . - ICSE Class 10 - Mathematics

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Question

In the figure, given below, find: (i) ∠BCD, (ii) ∠ADC, (iii) ∠ABC, Show steps of your working .

Solution

(i) ∠BCD + ∠BAD = 180°
(Sum of opposite angles of a cyclic quadrilateral is 180° )
⇒ ∠BCD= 180° -105° = 75°

(ii) Now, AB ∥ CD
∴ ∠BAD + ∠ADC = 180°
(Interior angles on the same side of parallel lines is 180° )
⇒∠ADC =180° -105° = 75°

(iii) ∠ADC +∠ABC = 180°
(Sum of opposite angles of a cyclic quadrilateral is 180°)
⇒∠ABC = 180° - 75° = 105°

  Is there an error in this question or solution?
Solution In the Figure, Given Below, Find: (I) ∠Bcd, (Ii) ∠Adc, (Iii) ∠Abc, Show Steps of Your Working . Concept: Cyclic Properties.
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