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
