Answer :
[tex]The\ angle\ (4y-8)^o\ and\ (79+y)^o\ are\ vertical\ angles\\\\therefore:\\\\(4y-8)^o=(79+y)^o\\4y-8=79+y\ \ \ \ |add\ 8\ to\ both\ sides\\4y=87+y\ \ \ \ |subtract\ "y"\ from\ both\ sides\\3y=87\ \ \ \ |divide\ both\ sides\ by\ 3\\\boxed{y=29^o}[/tex]
The angles at the opposite sides of point R are vertical opposite angles
The value of y in the figure is 29
Vertical angles are equal.
So, we have:
4y - 8 = 79 + y
Collect like terms, in the above equation
4y - y = 79 + 8
Evaluate the like terms
3y = 87
Divide both sides by 3
y = 29
Hence, the value of y in the figure is 29
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