Answer:
x = 45
Step-by-step explanation:
Since ray IK║EH and IG is a transverse,
∠GIK ≅ ∠IGF [Corresponding angles]
Therefore, m∠IGF = x
Since, m∠JIF + m∠GIF = 180° [Supplementary angles]
2x + m∠GIF = 180°
m∠GIF = (180 - 2x)
Similarly, m∠IFE + m∠IFG = 180°
3x + m∠IFG = 180°
m∠IFG = (180 - 3x)
By the property of a triangle,
"Sum of all interior angles of a triangle is 180°"
m∠IGF + m∠GFI + m∠FIG = 180°
x° + (180 - 2x)° + (180 - 3x)° = 180°
(x - 2x - 3x) + 360 = 180
-4x + 360 = 180
4x = 360 - 180
4x = 180
x = 45
