Respuesta :
Two angles are complementary if their measures add up to 90 degrees and are sumpplementary if their measures add up to 180 degrees.
From the image, we notice that the angles:
[tex]\angle GJH\text{ and }\angle EJG[/tex]These angles add up to 180 degrees because line JG bisects line HE at a 90 degrees angle, therefore, they are supplementary.
For angles
[tex]\angle IJH\text{ and }\angle FJH[/tex]These angles are supplementary because their measures add up to 180 degrees.
For angles:
[tex]\angle FJD\text{ and }\angle FJG[/tex]These are neither supplementary nor complementary because line GD is not a straight line.
For angles:
[tex]\angle IJH\text{ and }\angle FJG[/tex]We have the following relationship for these angles:
[tex]\angle IJH+\angle GJH+\angle FJG=180[/tex]Since angle GJH is 90 degrees we have:
[tex]\angle IJH+90+\angle FJG=180[/tex]Subtracting 90 to both sides:
[tex]\begin{gathered} \angle IJH+90-90+\angle FJG=180-90 \\ \angle IJH+\angle FJG=90 \end{gathered}[/tex]Therefore, their sum is 90 degrees and therefore they are complementary.
