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Sagot :
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°
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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