The lines CA and EF are parallel. Also, Both lines intersect the transversal line DH.
Now, the angles m∠BGA, m∠GAB and m∠ABG represent a triangle.
The measures of interior angles of a triangle sum to 180 degrees.
If m∠BGA = 52 and m∠GAB = 70.
Then
m∠BGA + m∠GAB + m∠ABG = 180
Replacing the angles values:
52 + 70 + m∠ABG = 180
Solve for m∠ABG
122 + m∠ABG = 180
m∠ABG = 180-122
m∠ABG = 58
To find m∠AGF, we need to know that angles m∠BGE, m∠ABG, and m∠AGF represent a straight line. Also, "Angles on a straight line add up to 180°."
Therefore:
m∠BGE + m∠BGA + m∠AGF = 180
If m∠BGE = 58 and m∠ABG = 58, we can replace these values and solve for m∠AGF.
Hence:
58 + 52 + m∠AGF = 180
110 + m∠AGF = 180
Solving for m∠AGF
m∠AGF = 180 - 110
m∠AGF = 70
