2 Missing Angles in a Polygon

Adam Keer
17 Jun 201602:29

Summary

TLDRIn this video, the presenter demonstrates how to calculate a missing angle in a polygon. Using the formula (n-2) * 180, they determine the total degrees in a five-sided pentagon to be 540°. By subtracting the known angles (112°, 130°, 96°, and 105°) from the total, the missing angle is calculated to be 97°. The video emphasizes checking the work by adding all angles to ensure they sum to 540°.

Takeaways

  • 📝 The video demonstrates how to find a missing angle in a polygon.
  • 📏 It begins by recalling the formula (n - 2) * 180 to determine the total degrees in a polygon.
  • 🔺 For this example, a pentagon (5-sided shape) is used.
  • 🔢 The calculation starts with n = 5, leading to (5 - 2) * 180 = 540°.
  • 📐 This means the total internal angles of the pentagon add up to 540°.
  • ➖ To find the missing angle, subtract the known angles from 540°.
  • ✏️ The known angles are: 112°, 130°, 96°, and 105°.
  • 🔍 Subtracting these from 540° leaves the missing angle, y, which is calculated to be 97°.
  • ✅ The result is verified by ensuring the sum of all angles equals 540°.
  • 🔚 The method is summarized: use the total degree formula, subtract known angles, and check the sum for accuracy.

Q & A

  • What is the formula used to find the total sum of interior angles in a polygon?

    -The formula is (n - 2) * 180, where n is the number of sides in the polygon.

  • How many sides does the polygon in the example have?

    -The polygon in the example is a pentagon, which has 5 sides.

  • How do you calculate the total sum of the interior angles for a pentagon?

    -For a pentagon, n is 5. Using the formula (n - 2) * 180, we get (5 - 2) * 180 = 3 * 180 = 540 degrees.

  • What is the first step in finding the missing angle in the polygon?

    -The first step is to calculate the total sum of the interior angles of the polygon using the formula.

  • How do you determine the missing angle once you have the total sum of the interior angles?

    -Subtract the sum of the known angles from the total sum of the interior angles.

  • What are the known angles in the example provided?

    -The known angles are 112 degrees, 130 degrees, 96 degrees, and 105 degrees.

  • How do you find the value of the missing angle?

    -Subtract the sum of the known angles from 540 degrees: 540 - (112 + 130 + 96 + 105).

  • What is the value of the missing angle in the example?

    -The missing angle is 97 degrees.

  • How can you verify the correctness of the calculated missing angle?

    -Add the missing angle to the known angles and ensure the total is 540 degrees.

  • What should you do if the sum of the angles does not equal the total calculated sum of interior angles?

    -If the sum is incorrect, recheck your calculations for any errors in the steps.

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Ähnliche Tags
GeometryMathematicsPolygonPentagonAnglesEducationalTutorialDegreesCalculationProblem-Solving
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