Mathematics
In the given figure, ∠ACB = 52° and= ∠BDC = 43°. Calculate
(i) ∠ADB
(ii) ∠BAC
(iii) ∠ABC.
Circles
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Answer
(i) From figure,
∠ADB = ∠ACB = 52° [Angles in the same segment are equal]
∠ADB = 52°.
Hence, ∠ADB = 52°.
(ii) From figure,
∠BAC = ∠BDC = 43° [Angles in the same segment are equal]
∠BAC = 43°.
Hence, ∠BAC = 43°.
(iii) We know that,
The sum of the three interior angles of any triangle is always 180°.
⇒ ∠BAC + ∠ABC + ∠ACB = 180°
⇒ 43° + ∠ABC + 52° = 180°
⇒ ∠ABC + 95° = 180°
⇒ ∠ABC = 180° - 95°
⇒ ∠ABC = 85°.
Hence, ∠ABC = 85°.
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