Answer:
The measure of angle AGF is [tex]59\°[/tex]
Step-by-step explanation:
Let
x------> the measure of angle CGD
y------> the measure of angle BGC
we know that
[tex]x+y+67\°=180\°[/tex] -----> equation A
[tex]x=y+5\°[/tex] -----> equation B
Substitute equation B in equation A and solve for y
[tex]y+5\°+y+67\°=180\°[/tex]
[tex]2y=180\°-72\°[/tex]
[tex]2y=108\°[/tex]
[tex]y=54\°[/tex]
Find the value of x
[tex]x=54\°+5\°=59\°[/tex]
The measure of angle CGD is [tex]59\°[/tex]
m<AGF=m<CGD -------> by vertical angles
therefore
The measure of angle AGF is [tex]59\°[/tex]
