Mathematics
Assertion (A): In the adjoining figure, ABCD is a cyclic quadrilateral. If ∠CBE = 108°, then ∠ADC = 108°.
Reason (R): In a cyclic quadrilateral, opposite angles are supplementary.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
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Answer
From figure,
∠CBE and ∠CBA forms a linear pair.
⇒ ∠CBE + ∠CBA = 180°
⇒ 108° + ∠CBA = 180°
⇒ ∠CBA = 180° - 108°
⇒ ∠CBA = 72°
ABCD is a cyclic quadrilateral, opposite angles are supplementary.
So, reason (R) is true.
⇒ ∠CBA + ∠ADC = 180°
⇒ 72° + ∠ADC = 180°
⇒ ∠ADC = 180° - 72°
⇒ ∠ADC = 108°.
So, assertion (A) is true.
Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Hence, option 3 is the correct option.
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