Question

Angle ABC is inscribed in circle p the length of PC is 12 units the arc length of a c is 68/15 pi what is the measure of angle ABC in degrees

Answer 1

here is the answer, first find the circumference and then use the formula i've written there

Answer 2

68°

Explanation:

The formula for arc length when central angle is in degrees =

Arc length = 2πr × θ /360

Arc length = 68/15π

Radius = the length of PC = 12 units

Hence:

68/15π = 68π/15 = 2 × π × 12 × θ /360

68π/15 = 75.4 ×θ /360

Cross Multiply

68π × 360 = 15 × 75.4 × θ

θ = 68π × 360/15 × 75.4

= 67.998398019°

Approximately = 68°

Therefore, the measure of central angle = 68°