what is the measure of <AGC?

Answer:
<AGC = 90°, the measure of <AGC is 90°.
Step-by-step explanation:
Supplementary angles are angles when added up is equal to to 180, they are supplementary if they are adjacent to each other meaning they have a common side and vertex.
Line EC, which angle AGC and angle AGE had a common side and vertex, meaning they are supplementary angles.
Therefore,
<AGC + <AGE = 180°
<AGC + 90° = 180°
<AGC = 180°- 90°
<AGC = 90°