Mathematics
In the figure (i) given below, AT is tangent to a circle at A. If ∠BAT = 45° and ∠BAC = 65°, find ∠ABC.
Circles
ICSE
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Answer
From figure,
∠ACB = ∠BAT = 45° (∵ angles in alternate segments are equal)
Since sum of angles in a triangle = 180°.
In △ABC,
⇒ ∠ACB + ∠CAB + ∠ABC = 180°
⇒ 45° + 65° + ∠ABC = 180°
⇒ 110° + ∠ABC = 180°
⇒ ∠ABC = 180° - 110°
⇒ ∠ABC = 70°.
Hence, the value of ∠ABC = 70°.
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