Réponse:

On note A, B, C, D, E, F et G les differents sommets des triangles (voir figure jointe)

ABC est isocele donc l'angle ACB = x

ABC = 180-(x+x) = 180-2x

L'angle ABD est plat

CBD= ABD-ABC

CBD = 180-(180-2x) = 2x

BCD est isocele :

BDC = CBD = 2x

BCD = 180 - 2×2x

BCD = 180-4x

DCE = 180 - (ACB+BCD)

DCE = 180 -( x + 180-4x)

DCE = 3x

CDE est isocele

DEC = DCE = 3x

CDE = 180 - 2×3x = 180 - 6x

EDF = 180 - (CDB + CDE)

EDF = 180 - (2x + 180-6x)

EDF = 4x

EDF est isocèle

DFE = EDF = 4x

DEF = 180 - 2×4x

DEF = 180-8x

FEG = 180 - ( DEC+DEF)

FEG = 180 - (3x + 180-8x)

FEG = 5x

FEG est isocele

EGF = FEG = 5x

EFG = 180 - 2×5x

EFG = 180-10x

DFG = DFE+EFG

90 = 4x + 180-10x

6x = 90

x = 90/6

x = 15