Question

What is the value of x in the equation

m∠FEG=82 and m∠FEC=5x+11 if the sum of these two angles is 180 degrees?

A) x=82
B) x=11
C) x=149
D)x=87/5
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Answer 1

To solve for x, we use the fact that the sum of angles FEG and FEC is 180 degrees. We set up the equation 82 + (5x + 11) = 180, simplify it, and solve for x, obtaining x = 87/5, which is answer choice D).

Step-by-step explanation:

To find the value of x in the given problem, we need to set up an equation using the information that the sum of the angles m∠FEG and m∠FEC is 180 degrees. Since m∠FEG is given as 82 degrees, and m∠FEC is given as 5x + 11, we can write the equation:

82 + (5x + 11) = 180.

Simplifying the equation:

93 + 5x = 180
5x = 180 - 93
5x = 87
x = 87/5

Therefore, the value of x is 87/5, which is choice D).