Question

What is the arc measure of \stackrel{\LARGE{\frown}}{BC}

Answer 1

Answer:

$\stackrel{\LARGE{\frown}}{BC} = 131$

Explanation:

Given

See attachment

Required

Find $\stackrel{\LARGE{\frown}}{BC}$

First, we need to determine the value of y. This is calculated as:

$4y+6 + 7y-7+20y-11 = 360$ --- angles in a circle

Collect like terms

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

$31y = 372$

Solve for y

$y = 372/31$

$y = 12$

The measure of $\stackrel{\LARGE{\frown}}{BC}$ is calculated as:

$\stackrel{\LARGE{\frown}}{BC} = \stackrel{\LARGE{\frown}}{BA} + \stackrel{\LARGE{\frown}}{AC}$

$\stackrel{\LARGE{\frown}}{BC} = 4y + 6 + 7y - 7$

Collect like terms

$\stackrel{\LARGE{\frown}}{BC} = 4y + 7y + 6 - 7$

$\stackrel{\LARGE{\frown}}{BC} = 11y -1$

Substitute $y = 12$

$\stackrel{\LARGE{\frown}}{BC} = 11*12 -1$

$\stackrel{\LARGE{\frown}}{BC} = 131$