Answer:
The value of x is 16.5.
Step-by-step explanation:
To solve this problem, we first must recognize the relationship between the given angles. There are many ways to determine this relationship - here I will give you just one. First, you can see that Angle 2 and Angle 4 are corresponding angles, so they must have the same measurement. Since, Angle 4 and Angle 8 are adjacent supplementary angles, the sum of their measurements must add up to 180 degrees. Since we know that Angle 2 and Angle 4 have the same measurement, this means that the sum of Angle 2 and Angle 8 must also equal 180 degrees.
Using this knowledge, we can write the following equation and substitute in the given values.
m<2 + m<8 = 180
107 + (4x + 7) = 180
Now, we can solve the equation for x.
107 + (4x + 7) = 180
114 + 4x = 180
4x = 66
x = 16.5
Therefore, the value of x is 16.5. To check your answer, you can plug this value for x back into the original equation.
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