Mathematics
Grade 10
15 min
Interior angles of polygons
Interior angles of polygons
What you'll learn
- Identify the labels on the x-axis and y-axis of a line graph and explain what each axis represents with 100% accuracy.
- Read and interpret data points on a line graph to answer at least 4 out of 5 questions about the information presented.
- Solve problems by using information displayed on a line graph to determine changes in data over time, achieving at least 80% accuracy.
- Explain the trend shown on a line graph (increasing, decreasing, or constant) in their own words, providing specific examples from the graph with 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the sum of the measures of the interior angles of any convex polygon.
Derive the formula for the sum of interior angles by dividing a polygon into triangles.
Determine the measure of a single interior angle of a regular polygon.
Solve for unknown angle measures in irregular polygons using the interior angle sum theorem.
Determine the number of sides of a polygon given the sum of its interior angles.
Apply the interior angle sum theorem to solve multi-step geometric problems and justify steps in a proof.
Ever wondered why honeycombs are made of perfect hexagons and not pentagons or squares? 🐝 The secret lies in the geometry of their interior angles!
In this tutorial, we will explore the relationship between the number of sides a polygon has and...
2
Key Concepts & Vocabulary
TermDefinitionExample
PolygonA closed two-dimensional figure made up of three or more straight line segments (sides) that meet only at their endpoints (vertices).A triangle (3 sides), a quadrilateral (4 sides), a pentagon (5 sides).
Interior AngleAn angle formed inside a polygon by two adjacent sides.In a square, each of the four interior angles measures 90 degrees.
Convex PolygonA polygon in which all interior angles are less than 180 degrees. All vertices point 'outwards', and any line segment connecting two vertices lies entirely inside the polygon.A standard stop sign (octagon) is a convex polygon.
Regular PolygonA polygon that is both equilateral (all sides are equal in length) and equiangular (all interior angles are equal in measure).A perfect square, an equilateral trian...
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Core Formulas
Polygon Interior Angle Sum Theorem
S = (n - 2) \times 180^{\circ}
Use this formula to find the sum (S) of the measures of the interior angles of any convex polygon with 'n' sides. The (n-2) part represents the number of triangles you can divide the polygon into from a single vertex.
Measure of an Interior Angle of a Regular Polygon
A = \frac{(n - 2) \times 180^{\circ}}{n}
Use this formula to find the measure of a single interior angle (A) of a regular n-gon. It works by taking the total sum of the angles and dividing it equally among the 'n' congruent angles.
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Sign Up Free to ContinueSample Practice Questions
Easy
Which formula correctly calculates the sum (S) of the measures of the interior angles of a convex polygon with 'n' sides?
A.S = n × 180°
B.S = (n - 2) × 180°
C.S = (n + 2) × 180°
D.S = 360° / n
Easy
What is the sum of the measures of the interior angles of a convex octagon?
A.900°
B.1440°
C.1080°
D.720°
Easy
What two properties must a polygon have to be considered a regular polygon?
A.It is convex and has an even number of sides.
B.All sides are parallel and all angles are acute.
C.It has at least five sides and all vertices point outwards.
D.All sides are equal in length and all interior angles are equal in measure.
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Frequently asked questions
What grade level is "Interior angles of polygons"?
Interior angles of polygons is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Interior angles of polygons?
You'll be able to: Identify the labels on the x-axis and y-axis of a line graph and explain what each axis represents with 100% accuracy; Read and interpret data points on a line graph to answer at least 4 out of 5 questions about the information….
Is "Interior angles of polygons" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Interior angles of polygons?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.