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°.

80

step-by-step explanation:

the answer to your question is minor arc.