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Solution Steps

Triangle ABC is isosceles with AC = BC. Therefore, angles CAB and CBA are equal. Angle ACB is given as 15°. Since the sum of angles in a triangle is 180°, angles CAB and CBA are both equal to (180° - 15°)/2 = 82.5°. α is angle CAB, so α = 82.5°.

Triangle DEF is isosceles with DF = FE. Therefore, angles FDE and FED are equal. Angle DFE is given as 110°. Since the sum of angles in a triangle is 180°, angles FDE and FED are both equal to (180° - 110°)/2 = 35°. β is angle FED, so β = 35°.

Triangle GHI is isosceles with GI = HI. Therefore, angles GHI and IGH are equal. Angle GHI is given as 24°. Since the sum of angles in a triangle is 180°, angle IGH is also 24°. Angle GIH, represented by γ, is equal to 180° - (24° + 24°) = 132°. So, γ = 132°.

Final Answer