Answer:
x ∈ {−0.766664695962, 2, 4}
Step-by-step explanation:
The equation is a combination of polynomial and exponential functions. There are no algebraic methods for solving such an equation. Graphical and iterative methods work nicely, though.
The attached graph shows integer solutions at x=2 and x=4. There is also an irrational negative solution near x = −0.766664695962. The latter was found by using Newton's method iteration on the graphical value of -0.767.
The measure of angle ∠EGF is 65°. And the measure of the angle ∠CGE is 115°.
<h3>What is the triangle?</h3>A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
Triangle GEF is shown with its exterior angles.
Line GF extends through point B.
Line FE extends through point A.
Line EG extends through point C.
Angles ∠FEG and ∠EGF are congruent.
∠FEG = ∠EGF = x
Sides EF and GF are congruent.
Angle ∠EFG is 50° degrees.
∠EFG + ∠FGE + ∠GEF = 180°
50° + x + x = 180°
2x = 130°
x = 65°
∠FEG = ∠EGF = 65°
Then angle ∠CGF will be
∠CGF + ∠FGE = 180°
∠CGF + 65° = 180°
∠CGF = 115°
More about the triangle link is given below.
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