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

Explanation:

Step1: Sum the central angles

The sum of all central angles in a circle is $360^{\circ}$. $$(4y + 6) + (7y - 7) + (20y - 11) = 360$$

Step2: Combine like terms

Combine the $y$ terms and the constant terms. $$31y - 12 = 360$$

Step3: Solve for $y$

Add 12 to both sides and divide by 31. $$31y = 372$$ $$y = 12$$

Step4: Calculate the measure of arc $BC$

The measure of minor arc $\widehat{BC}$ is equal to the central angle $\angle BPC$. $$m\widehat{BC} = (4y + 6) + (7y - 7) = 11y - 1$$

Step5: Substitute the value of $y$

Substitute $y = 12$ into the expression for $m\widehat{BC}$. $$m\widehat{BC} = 11(12) - 1 = 132 - 1 = 131$$

Answer:

131^{\circ}