Answer:
x = 3
y = 60°
Step-by-step explanation:
The given parameters of the figures are;
The sum of the interior angles of each polygon (quadrilaterals) = 360°
Quadrilateral ABCD = Quadrilateral HGEF
∴ ABCD ≅ HGEF
Therefore;
Segment AB ≅ Segment HG, by Corresponding Sides of congruent polygons are congruent
∴ The length of segment AB = 3 ft. = The length of segment HG = x ft.
∴ 3 ft. = x ft.
x = 3
Similarly, we have;
∠A + ∠B + ∠C + ∠D = 360° Given
∠B = 100°, and ∠D = 70° Given
∴ ∠A + ∠C = 360° - (∠B + ∠D) = 360° - (100° + 70°) = 190°
∠A + ∠C = 190°
∠A ≅ ∠G and ∠C ≅ ∠E Corresponding angles of congruent polygons are congruent
∴ ∠A = ∠G and ∠C = ∠E By definition of congruency
∴ ∠A + ∠C = ∠G + ∠E = 190° by transitive property
∠G = (2·y + 2)°, and ∠E = (y + 8)° Given
∴ ∠G + ∠E = (2·y + 2)° + (y + 8)° = (3·y + 10)° = 190°
3·y = 190° - 10° = 180°
y = 180°/3 = 60°
y = 60°