What is m ∠bac if the measure of arc ac = 76°?
76 degrees
152 degrees
38 degrees
104 degrees

Option C is correct.  

Step-by-step explanation:

Given: measure of arc AC= 76°

To find: ∠BAC

Figure is attached.

Circle with center O

Measure of arc AC = 76°

⇒ ∠AOC = 76°

ΔAOC is an isosceles triangle because OC = OA are radius.

⇒ ∠OAC =  ∠OCA  (angles opposite to equal sides are equal)

In Δ AOC,

∠AOC + ∠OAC + ∠OCA  = 180 (Angle sum property of triangle)

∠AOC + ∠OAC + ∠OAC  = 180

76 + 2∠OAC = 180

2∠OAC = 104

∠OAC = 52°

AB is tangent to circle.

using result, which states that Radius and tangent are perpendicular at point of contact.

we get,

∠OAB = 90°

∠BAC + ∠OAC = 90

∠BAC + 52 = 90

∠BAC = 38°

Therefore, Option C is correct.