Answer:
x = 51°
Step-by-step explanation:
∠ABF = ∠CBD = x° → Vertical angles
ΔBCD:
∠BDC + x° + 28° = 180° → total angles in a triangle = 180°
∠BCD = (152 - x)°
∠EDB + ∠BCD = 180° → Supplementary angles
∠EDB + (152 - x)° = 180°
∠EDB = (28 + x)°
ABDE is a cyclic quadrilateral (quadrilateral which all 4 vertices are on the perimeter of the circle) → the total angles of opposite angles = 180°
∠EAB + ∠EDB = 180°
∠EAB + (28 + x)° = 180°
∠EAB = (152 - x)°
∠FAB + ∠EAB = 180° → Supplementary angles
∠FAB + (152 - x)° = 180°
∠FAB = (28 + x)°
ΔFAB:
∠FAB + ∠ABF + ∠AFB = 180° → total angles in a triangle = 180°
(28 + x)° + x° + 50° = 180°
78° + 2x° = 180°
2x° = 102°
x = 51°
