VTriangle EFG is similar to triangle IHG in the figure shown below.

What is the measure of angle EFG ?

33°

55°

59°

88°

m∠EFG = 59°

Solution:

Given ∠HGI = 33°, ∠GIH = 88°

In ΔIHG,

Sum of the angles of the triangle = 180°

⇒ ∠HGI + ∠GIH + ∠IHG = 180°

⇒ 33° + 88° + ∠IHG = 180°

⇒ ∠IHG = 180° – 121°

⇒ ∠IHG = 59°

EF || IH and FH is a transversal.

Alternative interior angle theorem:

If two parallel lines cut by a transversal then their alternative interior angles are congruent.

By alternative interior angle theorem,  

∠EFG = ∠IHG

∠EFG = 59°

Hence the measure of angle EFG = 59°.

4.6875 pounds

step-by-step explanation:

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: