Answer:
∠BCE is 115°
Step-by-step explanation:
The given parameters are;
The shape Tanya cut from the striped piece = Isosceles triangles
The measure of the vertex angle of the isosceles triangle = 50°
The segment [tex]\overline {BC}[/tex] is parallel to the base [tex]\overline {FG}[/tex]
Therefore, we have;
∠GAF + ∠AGF + ∠AFG = 180°; Sum of the interior angles of a triangle
∴ ∠AGF + ∠AFG = 180° - ∠GAF = 180° - 50° = 130°
∠AGF = ∠AFG; Base angles of an isosceles triangle
∴ ∠AGF + ∠AFG = ∠AGF + ∠AGF = 2 × ∠AGF = 130°
∠AGF = 130°/2 = 65°
∠AGF = 65°
∠AGF ≅ ∠ACB, corresponding angles of two parallel lines, [tex]\overline {BC}[/tex] and [tex]\overline {FG}[/tex] cut by a transversal [tex]\overline {AG}[/tex]
∠AGF = ∠ACB = 65°, definition of congruency
∠ACB + ∠BCE = 180° Sum of angles on a (straight) line
∠BCE = 180° - ∠ACB = 180° - 65° = 115°
∠BCE = 115°
