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[tex]\bold {PROBLEM:}[/tex]
Trapezoid FINE is isosceles with bases FE and IN. If ∠IFE = 4x-15 and ∠FEN = 7x-105, what is ∠ENI?
[tex]\bold {SOLUTION:}[/tex]
Given that the FE and IN are the bases, ∠IFE and ∠FEN are consecutive angles on the base of the trapeziod, thus, they are congruent. We will use their relationship to find the value of x.
[tex] \large \tt \angle IFE\cong\angle FEN \\ \\ \large \tt m\angle IFE = m\angle FEN \\ \\ \large \tt 4x - 15 = 7x - 105 \\ \\ \large \tt 4x - 7x = - 105 + 15 \\ \\ \large \tt - 3x = - 90 \\ \\ \large \tt \frac{ - 3x}{ - 3} = \frac{ - 90}{ - 3} \\ \\ \large \red{ \boxed{ \tt x = 30}}[/tex]
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