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

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

TODETERMINE∠ENI

EVALUATIONHere 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°

FINALANSWER∠ENI = 150°━━━━━━━━━━━━━━━━Learn more from Brainly :-[tex]1.[/tex] The angles of the triangle are 3x–40, x+20 and 2x–10 then the value of x is

(a) 40 (b) 35 (c) 50 (d) 45

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2. The difference between an angle and its complement is 10° find measure of larger number.

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