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

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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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