Question

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

Answer 1

SOLUTION

GIVEN

Trapezoid FINE is isosceles with bases FE and IN. If ∠IFE = 4x - 15° and ∠FEN = 7x - 105°

TO DETERMINE

∠ENI

EVALUATION

Here it is given that Trapezoid FINE is isosceles with bases FE and IN.

Now ∠IFE = 4x - 15° and ∠FEN = 7x - 105°

We know that angles on the same base are congruent.

∴ ∠IFE = ∠FEN

⇒ 4x - 15° = 7x - 105°

⇒ 3x = 90°

⇒ x = 30°

Now we have to find ∠ENI

We know in case of an isosceles trapezoid opposite angles are supplementary

∴ ∠ENI = 180° - 30° = 150°

FINAL ANSWER

∠ENI = 150°

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