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 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.