In the following figure, ΔABC is an inscribed triangle as shown and DE is a tangent to the circle at C. If m∠ACD = 65^o and m∠ACB = 35^o, find the measure of m∠BAC ?

80^o

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