Mathematics
In the given figure, PAT is tangent at A. If ∠TAB = 70° and ∠BAC = 45°, find ∠ABC.
Circles
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Answer
From figure,
∠ACB = ∠TAB = 70° [Angles in the alternate segment are equal]
In ΔABC,
⇒ ∠ACB + ∠BAC + ∠ABC = 180° [By angle sum property of triangle]
⇒ ∠ABC = 180° - (∠BAC + ∠ACB)
⇒ ∠ABC = 180° - (45° + 70°)
⇒ ∠ABC = 65°.
Hence, ∠ABC = 65°.
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