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The sum of the interior angles of each polygon is 360°. In the diagram ABCD=HGEF find the values of x and y look at photo below

The sum of the interior angles of each polygon is 360 In the diagram ABCDHGEF find the values of x and y look at photo below class=

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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°

The value of x and y are 3 feet and 72 degrees respectively

Angle in a quadrilateral.

From the given quadrilaterals, the sum of adjacent angles is 180 degrees.

Hence from figure;

  • m<E + m<F = 180
  • m<B = m<F = 100

y + 8 + 100 = 180

y + 108 = 180

y = 180 - 108

y = 72degrees

Similarly;

m<D = mG = 70 degrees.

AB = GH = 3 feet

Hence the value of x and y are 3 feet and 72 degrees respectively

Learn more on Angle in a quadrilateral here: https://brainly.com/question/10975107