Question

The lines s and t intersect at point R.

What is the value of y?

y =

Answer 1

$The\ angle\ (4y-8)^o\ and\ (79+y)^o\ are\ vertical\ angles\\\\therefore:\\\\(4y-8)^o=(79+y)^o\\4y-8=79+y\ \ \ \ |add\ 8\ to\ both\ sides\\4y=87+y\ \ \ \ |subtract\ "y"\ from\ both\ sides\\3y=87\ \ \ \ |divide\ both\ sides\ by\ 3\\\boxed{y=29^o}$

Answer 2

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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