A pentagon has actually 5 sides, and also can it is in made from three triangles, for this reason you recognize what ...
You are watching: Angles of a quadrilateral add up to
... Its interior angles add up to 3 × 180° = 540°
And once it is regular (all angle the same), then each angle is 540° / 5 = 108°
(Exercise: make certain each triangle here adds approximately 180°, and check that the pentagon\"s internal angles add up come 540°)
The inner Angles that a Pentagon add up to 540°
The basic Rule
Each time we add a next (triangle to quadrilateral, square to pentagon, etc), us add another 180° to the total:
|If that is a Regular Polygon (all sides space equal, all angles are equal)|
|Heptagon (or Septagon)||7||900°||128.57...°|
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|Any Polygon||n||(n−2) × 180°||(n−2) × 180° / n|
So the general preeminence is:
Sum of inner Angles = (n−2) × 180°
Each edge (of a continuous Polygon) = (n−2) × 180° / n
Perhaps an instance will help:
Example: What about a constant Decagon (10 sides) ?
Sum of internal Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
And for a regular Decagon:
Each inner angle = 1440°/10 = 144°
Note: interior Angles room sometimes dubbed \"Internal Angles\"
inner Angles Exterior Angles degrees (Angle) 2D shapes Triangles quadrilaterals Geometry Index