Answer:
[tex]\stackrel{\LARGE{\frown}}{BC} = 131[/tex]
Explanation:
Given
See attachment
Required
Find [tex]\stackrel{\LARGE{\frown}}{BC}[/tex]
First, we need to determine the value of y. This is calculated as:
[tex]4y+6 + 7y-7+20y-11 = 360[/tex] --- angles in a circle
Collect like terms
[tex]4y + 7y+20y = -6 + 7 + 11+360[/tex]
[tex]31y = 372[/tex]
Solve for y
[tex]y = 372/31[/tex]
[tex]y = 12[/tex]
The measure of [tex]\stackrel{\LARGE{\frown}}{BC}[/tex] is calculated as:
[tex]\stackrel{\LARGE{\frown}}{BC} = \stackrel{\LARGE{\frown}}{BA} + \stackrel{\LARGE{\frown}}{AC}[/tex]
[tex]\stackrel{\LARGE{\frown}}{BC} = 4y + 6 + 7y - 7[/tex]
Collect like terms
[tex]\stackrel{\LARGE{\frown}}{BC} = 4y + 7y + 6 - 7[/tex]
[tex]\stackrel{\LARGE{\frown}}{BC} = 11y -1\\[/tex]
Substitute [tex]y = 12[/tex]
[tex]\stackrel{\LARGE{\frown}}{BC} = 11*12 -1[/tex]
[tex]\stackrel{\LARGE{\frown}}{BC} = 131[/tex]
