An equilateral triangle has three equal sides and three equal interior angles. Each angle is 60º or π/3 radians, adding up to 180º or π radians total.
A square has four equal sides and four equal interior angles. Each interior angle is 90º or π/2 radians, adding up to 360º or 2π radians total.
Interior Angles of PolygonsA short chart of additional polygons with their interior angles provides the following data:
Pentagon 5 interior angles of 108º (540º or 3π radians total)
Hexagon 6 interior angles of 120º (720º or 4π radians total)
Heptagon 7 interior angles of about 128.57º (900º or 5π radians total)
Octagon 8 interior angles of 135º (1080º or 6π radians total)
ф = (n-2)π radians or ф = (n-2)180º.But how do we know, without resorting to a formula, that a triangle possesses an interior angle total of 180º or π radians? And how can we use this example to establish at least one other polygon’s angular total?
Now draw a line that cuts across the x-axis at any angle. The figure demonstrates this. The two angles at the intersection above that axis add up to 180° or π radians. So if there are three angles total, say α and β and γ , then α + β + γ = 180°. That being said, note our second image.
But If All Is Not ClearBut if all of this still leaves you a bit in the dark, see the video below. And even if it doesn’t leave you in the dark, but you wish put an in-depth impress into mind… see the Khan Academy video below.
Note: You might also enjoy Is a Circle a Polygon or Not? Implications for Calculus
← Back to Math-Logic-Design