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

download Export
search_insights Statistics
stylus_note White Board
Quran
calculate Calculator
dictionary Dictionary
fullscreen Full Screen
QUESTION OF
Views #: 7
Questions #: 10
Time: 9 minutes
Pass Score: 80.0%
Style
Mode

The Angle-Sum Formula for a Polygon

1 pts
volume_mute

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°
note_alt Add notes
✕
flag Flag

Correct Answer

Explanation

Why Is the Angle Sum of a Quadrilateral 360°?

1 pts
volume_mute

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?

note_alt Add notes
✕
flag Flag

Correct Answer

Explanation

Sum of Angles of a Pentagon

1 pts
volume_mute

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?

note_alt Add notes
✕
flag Flag

Correct Answer

Explanation

Sum of Angles of a Hexagon

1 pts
volume_mute

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?

note_alt Add notes
✕
flag Flag

Correct Answer

Explanation

Find the Sum for a 13-Sided Polygon

2 pts
volume_mute

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

n = 13 sidesS = (13 − 2) · 180°= 11 · 180° = ?
note_alt Add notes
✕
flag Flag

Correct Answer

Explanation

Find the Sum for a 7-Sided Polygon

2 pts
volume_mute

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
note_alt Add notes
✕
flag Flag

Correct Answer

Explanation

Find the Number of Sides Given the Angle Sum

2 pts
volume_mute

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
note_alt Add notes
✕
flag Flag

Correct Answer

Explanation

Find the Number of Sides – Angle Sum 1,620°

2 pts
volume_mute

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

note_alt Add notes
✕
flag Flag

Correct Answer

Explanation

Complete the Derivation Pattern

2 pts

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°
note_alt Add notes
✕
flag Flag

Correct Answer

Explanation

Match Each Polygon to Its Angle Sum

2 pts

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

TriangleQuadrilateralPentagonHexagon

To complete the line match

  1. Click on an item in the first group
  2. Click on the match in the second group

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°
note_alt Add notes
✕
flag Flag

Correct Answer

Explanation

✕
0
sin cos tan
sin-1 cos-1 tan-1 π e
xy x3 x2 ex 10x
y√x 3√x √x ln log
( ) 1/x % n!
7 8 9 + MS
4 5 6 – M+
1 2 3 × M-
0 . EXP ÷ MR
± RND C = MC
Keywords
Year 9