circle $p$ is below.\nwhat is the arc measure of major arc $\\widehat{abc}$ in degrees?

Explanation:

Step1: Sum central angles to $360^{\circ}$

$$(4y + 6) + (7y - 7) + (20y - 11) = 360$$

Step2: Combine like terms

$$31y - 12 = 360$$

Step3: Solve for variable $y$

$$31y = 372 \implies y = 12$$

Step4: Identify major arc components

$$m\widehat{ABC} = m\angle{APB} + m\angle{BPC}$$

Step5: Substitute $y$ into expressions

$$m\widehat{ABC} = (4(12) + 6) + (20(12) - 11)$$

Step6: Calculate final arc measure

$$m\widehat{ABC} = 54 + 229 = 283$$

Answer:

283^{\circ}