We are given the following information
Line EF intersects line AB and line CD
GH ≅ IH
m∠EGB = 50° and m∠DIG = 115°
We are asked to explain that why line AB is parallel is line CD.
As you can see, corresponding angles are equal so, m∠GHI = m∠EGB = 50°
We know that angles on a straight line equal 180°
[tex]m\angle GIH=180-115=65\degree[/tex]
Therefore, in triangle GHI, angle H equals 50, angle I equals 65 and angle G equals 65
Angles in a triangle equals 180
Therefore, lines AB and CD are parallel
