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प्रश्न
In the figure, given below, find: ∠ADC, Show steps of your working.
उत्तर
Now, AB || CD
∴ ∠BAD + ∠ADC = 180°
(Interior angles on the same side of parallel lines is 180°)
`=>` ∠ADC = 180° – 105° = 75°
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An exterior angle of a cyclic quadrilateral is congruent to the angle opposite to its adjacent interior angle, to prove the theorem complete the activity.
Given: ABCD is cyclic,
`square` is the exterior angle of ABCD
To prove: ∠DCE ≅ ∠BAD
Proof: `square` + ∠BCD = `square` .....[Angles in linear pair] (I)
ABCD is a cyclic.
`square` + ∠BAD = `square` ......[Theorem of cyclic quadrilateral] (II)
By (I) and (II)
∠DCE + ∠BCD = `square` + ∠BAD
∠DCE ≅ ∠BAD
