The measure of arc BC is: 147°
What is the angle of the chord?
It would be that measure of arc BC is, in other words, m∠ BPC, respectively arc AD being ⇒ m∠ APD ~
By Vertical Angles Theorem, we can say that:
m∠ BPC = m∠ APD ⇒ provided AC and BD are diameters,
We have that:
m∠ BPC = (4k + 159)° ⇒ knowing mBC is, in other terms m∠ BPC,
m∠ APD = (2k + 153)° ⇒ knowing mAB is, in other terms m∠ APD,
Thus:
4k + 159 = 2k + 153
4k - 2k = 153 - 159
2k = -6
k = -3
Thus:
m∠ BPC = (4(-3) + 159)° = 147°
m∠ APD = (2(-3) + 153)° = 147°