In the following figure, ΔABC is an inscribed triangle as shown and DE is a tangent to the circle at C. If m∠ACD = 65o and m∠ACB = 35o, find the measure of m∠BAC ?
Answer & explanation
Correct answer: option 1
DE is a straight line. So,
∠ACD + ∠ACB + ∠BCE = 180º
65º + 35º + ∠BCE = 180º
∠BCE = 80º
By using alternate segment theorem, Which states that an angle between a tangent and a chord is equal to the angle made by the chord in the alternate segment of the circle.
So, ∠BCE = ∠BAC
We know ∠BCE = 80º
So, ∠BAC = 80º