Podcast
Questions and Answers
What is the relationship between an exterior angle and its adjacent interior angle in a polygon?
What is the relationship between an exterior angle and its adjacent interior angle in a polygon?
- They are supplementary, summing to 180°. (correct)
- They are equal.
- They are complementary, summing to 90°.
- Their sum depends on the number of sides of the polygon.
The sum of the exterior angles of a polygon depends on the number of sides.
The sum of the exterior angles of a polygon depends on the number of sides.
False (B)
What formula is used to calculate the sum of the interior angles of a polygon, given the number of sides (n)?
What formula is used to calculate the sum of the interior angles of a polygon, given the number of sides (n)?
(n-2) * 180
An _______ angle is formed between one side of a polygon and the extension of an adjacent side.
An _______ angle is formed between one side of a polygon and the extension of an adjacent side.
If a polygon has 8 sides, what is the sum of its interior angles?
If a polygon has 8 sides, what is the sum of its interior angles?
Why does drawing diagonals from one vertex of a polygon create n-2 triangles?
Why does drawing diagonals from one vertex of a polygon create n-2 triangles?
What does it mean for an exterior angle to be 'supplementary' to its adjacent interior angle?
What does it mean for an exterior angle to be 'supplementary' to its adjacent interior angle?
A pentagon has four interior angles measuring 100°, 110°, 120°, and 130°. What is the measure of the missing angle?
A pentagon has four interior angles measuring 100°, 110°, 120°, and 130°. What is the measure of the missing angle?
Flashcards
Exterior Angle
Exterior Angle
An angle formed by a polygon's side and the extension of its adjacent side, located outside the polygon.
Interior Angle
Interior Angle
An angle formed between two adjacent sides inside a polygon.
Exterior Angle Sum Theorem
Exterior Angle Sum Theorem
The sum of exterior angles of any polygon always equals 360 degrees.
Interior Angle Sum Formula
Interior Angle Sum Formula
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Pentagon
Pentagon
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Diagonal
Diagonal
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Find Polygon Interior Angle Sums
Find Polygon Interior Angle Sums
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Will the number of triangles change?
Will the number of triangles change?
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Interior Angle Sum
Interior Angle Sum
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Exterior Angle Sum
Exterior Angle Sum
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Diagonal of a Polygon
Diagonal of a Polygon
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Number of Triangles Change?
Number of Triangles Change?
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Missing Angle
Missing Angle
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Polygon Interior Angle Sum
Polygon Interior Angle Sum
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Study Notes
Find an Exterior Angle Measure cont...
- If m∠1 ≅ m∠3, m∠1 = 3x, and m∠2 = 2x (as in the diagram), you can equate them to 360
Find an Exterior Angle Measure cont...
- If m∠1 ≅ m∠3 ≅ m∠4 ≅ m∠6, m∠2 ≅ m∠5, and m∠3 = m∠2 + 30, then m∠4 = 70
Individual activity
- SAT/ACT The figure below is a regular polygon. What is the value of n? Round to the nearest whole number.
- Concave polygon is a polygon that has an interior angle greater than 180°
- A polygon that has no interior angles greater than 180° is a convex polygon
- A hexagon in which all angles measure 120° is an example of an equiangular polygon
- An octagon in which all angles measure 135° and all sides are 6 cm long is an example of a regular polygon
- An angle inside a polygon is an interior angle
Geometry Figures
- A figure with equal angled is equiangular
- A figure with equal sides is equilateral
Angles
- An exterior angle is not acute, not interior, and not straight
- A square is equiangular and equilateral
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Description
Presentation on polygon angle-sum theorems, covering exterior and interior angles. Objectives include calculating the sum of exterior angles (360°) and the sum of interior angles using the formula (n-2) * 180°. Includes vocabulary builder for exterior angles.
