Trapezoid FINE is isosceles with bases FE and IN. If m&ang;IFE = 4x-15 and m&ang;FEN= 7x-105, what is m&ang;ENI?a.105 b. 95 c.85 d. 75. Created by mich0345. Math

Trapezoid FINE is isosceles with bases FE and IN. If m∠IFE = 4x-15 and m∠FEN= 7x-105, what is m∠ENI?Property of an isosceles trapezoid: angles on the same base are congruent. We will use this relationship to find the value of x.Property of an isosceles trapezoid: opposite angles are supplementary, thus, m∠IFE and m∠ENI are supplementary. We will substitute the value of x to the given m∠IFE to find m∠ENI.

Trapezoid FINE is isosceles with bases FE and IN. If m∠IFE = 4x-15 and m∠FEN= 7x...

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chirilu

$\footnotesize\textsf{*An illustration of the trapeziod is attached above}$

$\bold{PROBLEM:}$

Trapezoid FINE is isosceles with bases FE and IN. If m∠IFE = 4x-15 and m∠FEN= 7x-105, what is m∠ENI?

$\bold{SOLUTION:}$

Property of an isosceles trapezoid: angles on the same base are congruent. We will use this relationship to find the value of x.

$\large \tt 4x - 15 = 7x - 105 \\ \\ \large \tt 4x - 7x = - 105 + 15 \\ \\ \large \tt - 3x = - 90 \\ \\ \large \tt \frac{ - 3x}{ - 3} = \frac{ - 90}{ - 3} \\ \\ \large \boxed{ \tt x = 30}$

Property of an isosceles trapezoid: opposite angles are supplementary, thus, m∠IFE and m∠ENI are supplementary. We will substitute the value of x to the given m∠IFE to find m∠ENI.

$\begin{array}{l} \large \tt m∠ENI + m∠IFE=180° \\ \\ \large \tt m∠ENI + 4x - 15 = 180° \\ \\ \large \tt m∠ENI + 4(30) - 15 = 180° \\ \\ \large \tt m∠ENI + 120 - 15 = 180° \\ \\ \large \tt m∠ENI + 105 = 180° \\ \\ \large \tt m∠ENI = 180 °- 105 \\ \\ \large \red {\boxed{ \tt m∠ENI = 75°}} \end{array}$

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anthony0306 ate pahelp po huhu

cesalthea

Answer:

c.85

Step-by-step explanation:

mich0345 How can you be sure that 85 is the correct answer?

cesalthea yes

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