Use the formula for the sum of the angle measures of a polygon

The total sum of all the interior angles inside a polygon depends entirely on the number of sides it has

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Views #: 223
Questions #: 10
Time: 9 minutes
Pass Score: 80.0%
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The Angle-Sum Formula for a Polygon

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The sum \(S\) of the measures of the angles of a polygon with \(n\) sides is given by the formula:

\[ S = (n - 2) \cdot 180° \]

What does the variable \(n\) represent in this formula?

s₁s₂s₃s₄s₅n = 5 sidesS = (5−2)·180° = 540°
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Why Is the Angle Sum of a Quadrilateral 360°?

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A quadrilateral can be divided into triangles by drawing a diagonal, as shown below. Each triangle has an angle sum of 180°.

ABCD① 180°② 180°

How many triangles is the quadrilateral divided into, and what is the total sum of its angle measures?

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Sum of Angles of a Pentagon

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The pentagon below is divided into triangles by drawing diagonals from vertex \(A\).

ABCDE①②③

What is the sum of the angle measures of the pentagon?

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Sum of Angles of a Hexagon

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The hexagon below is divided into triangles by drawing diagonals from vertex \(A\).

ABCDEF①②③④

What is the sum of the angle measures of the hexagon?

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Find the Sum for a 13-Sided Polygon

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Find the sum of the angle measures of a 13-sided polygon.

n = 13 sidesS = (13 − 2) · 180°= 11 · 180° = ?
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Find the Sum for a 7-Sided Polygon

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Find the sum of the angle measures of the 7-sided polygon shown below.

Find the sum of the angle measures of the 7-sided polygon shown below.

A B C D E F G n = 7 sides
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Find the Number of Sides Given the Angle Sum

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The sum of the angle measures of a polygon is 1,080°. How many sides does the polygon have?

S = 1,080°n = ?n sides
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Find the Number of Sides – Angle Sum 1,620°

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The sum of the angle measures of a polygon is 1,620°. How many sides does the polygon have?

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Complete the Derivation Pattern

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A polygon with \(n\) sides can be divided into \((n-2)\) triangles. Complete the table below by dragging the correct values:

PolygonSides (n)Triangles (n−2)Sum SQuadrilateral42360°Pentagon53540°Hexagon64720°

For an octagon (\(n = 8\)):

Number of triangles = 8 − 2 = (1)

Sum \(S\) = (1) × 180° = (2)

Please drag and drop the selected option in the right place or type it instead
6
1,080°
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Match Each Polygon to Its Angle Sum

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To complete the line match
  1. Click on an item in the first group
  2. Click on an item in the second group
  3. To delete a match, double click on a line

Polygon

Triangle (3 sides)
Quadrilateral (4 sides)
Pentagon (5 sides)
Hexagon (6 sides)

Angle Sum

720°
360°
540°
180°

Use the formula \(S = (n-2) \cdot 180°\) to match each polygon to its total angle sum.

TriangleQuadrilateralPentagonHexagon
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Keywords
Year 9