Mathematics
In the figure (i) given below, ABCD is a cyclic quadrilateral. If ∠ADC = 80° and ∠ACD = 52°, find the values of ∠ABC and ∠CBD.
Circles
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Answer
In the given figure,
ABCD is a cyclic quadrilateral.
Since, sum of opposite angles of a cyclic quadrilateral is 180°.
⇒ ∠ABC + ∠ADC = 180°
⇒ ∠ABC + 80° = 180°
⇒ ∠ABC = 180° - 80°
⇒ ∠ABC = 100°.
From figure,
∠DBA = ∠DCA = 52°. (∵ angles in same segment are equal.)
⇒ ∠ABC = ∠DBA + ∠CBD
⇒ 100° = 52° + ∠CBD
⇒ ∠CBD = 100° - 52°
⇒ ∠CBD = 48°.
Hence, ∠ABC = 100° and ∠CBD = 48°.
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