Question

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

BC

⌢

B, C, start superscript, \frown, end superscript in degrees?

Answer 1

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

Step-by-step 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`