Question

In the diagram below, overline AD || overline EH m angle I=54^ and m angle FBC=48^ . Find m angle IGF .

Answer 1

As line AD is parallel to EH, we can say they're cut by the transversal line BI.

Then, angle FBC and angle IFG are corresponding angles, and they're congruent which means they have the same measure (48°).

The sum of the interior angles of a triangle is 180°, then:

`\begin{gathered} m\angle I+m\angle IFG+m\angle IGF=180\degree \\ 54\degree+48\degree+m\angle IGF=180\degree \\ m\angle IGF=180\degree-54\degree-48\degree \\ m\angle IGF=78\degree \end{gathered}`

Answer: Angle IGF measures 78°