Based on the vertical angles theorem, the measure of angle is equal to 64°
In Mathematics and Euclidean Geometry, the linear pair theorem states that the measure of two angles would add up to 180° provided that they both intersect at a point or form a linear pair.
By applying the linear pair theorem to the figure, we can logically deduce the following supplementary angles:
m∠CIH + m∠GIH = 180°.
m∠GIH = 180° - 105
m∠GIH = 75°
Based on the vertical angles theorem, angle m∠BGD is congruent with m∠HGI;
m∠BGD ≅ m∠HGI
By applying angle sum property to triangle GHI, we have;
m∠GIH + m∠HGI + m∠GHI = 180°.
75 + 41 + m∠GHI = 180°.
m∠GHI = 180° - 116
m∠GHI = 64°
Based on the vertical angles theorem, angle m∠GHI is congruent with m∠AHF;
m∠GHI ≅ m∠AHF = 64°