Question : AC is the diameter of the circle. B is a point on the circumference. If $\angle$BAC is 40°, then what is $\angle$BCA?
Option 1: 50°
Option 2: 90°
Option 3: 55°
Option 4: 40°
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Correct Answer: 50°
Solution :
Given that AC is the diameter of the circle, B is a point on the circumference, and $\angle$ BAC = 40°
In $\triangle$ABC,
$ \angle$ BAC + $\angle$ ABC + $\angle $BCA = 180°
⇒ 40° + 90° + $\angle $BCA = 180°
⇒ $ \angle $BCA = 180° – 40° – 90° = 50°
Hence, the correct answer is 50°.
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