Make different types of 5 polygons and also find the sum of all angles by actual measurement.
Answers
Answer:
To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal.
Step-by-step explanation:
540°
The General Rule
Shape Sides Sum of Interior Angles
Triangle 3 180°
Quadrilateral 4 360°
Pentagon 5 540°
Hexagon 6 720°
Exterior Angles of a Regular Polygon with n sides: Exterior angle = 360°/n.
Let’s start with the idea that the sum of the angles of a triangle (in a plane) is 180°.
Below is an image that explains why this must be so.
Given △ABC with line j parallel to segment AC and passing through point B.
At B m∠1 + m∠2 + ∠3 = 180°.
m∠BAC = m∠1 because the alternate interior angles (AIA) formed by two parallel lines cut by a transversal are congruent.
Similarly m∠BCA = m∠3 because of AIA.
Therefore, the sum of the angles of a triangle on a plane is 180°. ☐
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