In the diagram, segment DA is tangent to the circle at point A, and segment DB is secant to the circle at points C and B. The rays intersect outside of the circle at point D to form ∠D, which intercepts arc AC and arc AB. If m∠D=81°, m of arc AB = (5x)°, and m of arc AC = (2x−21)°, what is the measure of arc AC? *
A.73°
B.64°
C.78°
D.81°

Quick Answer: A
Step One
You should have a diagram of this. My diagram looks like the one below.

Step Two
State the needed givens
D = 81
AC = 2x - 21
AB = 5x

Step Three
State the formula
1/2(Large Arc - Small Arc) = Angle meeting tangent and Secant

Step Four
Substitute and Solve
1/2(5x - (2x - 21)) = 81 Multiply by 2
(5x - (2x - 21)) = 162 Remove the brackets.
5x - 2x + 21 = 162 Combine like terms on the left
3x + 21 = 162 Subtract 21 from both sides.
3x = 162 - 21
3x = 141 Divide by 3
x = 141 / 3
x = 47

Step Five
Solve 2x - 21
2x - 21
2*47 -21
94 - 21
73 <<<<<< Answer.