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Answer :

Answer:

see explanation

Step-by-step explanation:

Since the marked angles are congruent, let them be x

(6)

The sum of the interior angles of a quadrilateral = 360°

Sum the angles and equate to 360

x + x + 120 + 90 = 360

2x + 210 = 360 ( subtract 210 from both sides )

2x = 150 ( divide both sides by 2 )

x = 75

Then ∠ X = ∠ Y = 75°

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(7)

The sum of the interior angles of a hexagon = 720°

Sum the angles and equate to 720

x + x + 108 + 103 + 149 + 90 = 720

2x + 450 = 720 ( subtract 450 from both sides )

2x = 270 ( divide both sides by 2 )

x = 135

Then ∠ X = ∠ Y = 135°

Mhanifago

Answer:

  • 6) x = 75°, y = 75°
  • 7) x = 135°, y = 135°

Step-by-step explanation:

Sum of the interior angles of a regular polygon:

  • S(n) = 180°(n - 2), where n- number of sides

Exercise 6

Quadrilateral has sum of angles:

  • S(4) = 180°(4 - 2) = 360°

Sum the given angles and consider x = y as marked congruent:

  • 2x + 120° + 90° = 360°
  • 2x + 210° = 360°
  • 2x = 360° - 210°
  • 2x = 150°
  • x = 75° and y = x = 75°

Exercise 7

Hexagon has sum of angles:

  • S(6) = 180°(6 - 2) = 720°

Sum the given angles and consider x = y as marked congruent:

  • 2x + 108° + 103° + 149° + 90° = 720°
  • 2x + 450° = 720°
  • 2x = 720° - 450°
  • 2x = 270°
  • x = 135° and y = x = 135°

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