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Angle sums of triangles & quadrilaterals

Basic shapes

Japanese school year: Elementary 5

What you learn

Learn that the interior angles of a triangle add up to 180 degrees, while those of a quadrilateral sum to 360 degrees. This fundamental property is essential for calculating unknown angles across various geometric figures. Reviewing angle measurement and the concept of straight angles will deepen your understanding.

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Key points

This formula states that the sum of interior angles in any triangle is always 180∘180^\circ. Here, ∠A\angle A, ∠B\angle B, and ∠C\angle C represent the three angles; knowing two gives the third.

∠A+∠B+∠C=180∘\angle A + \angle B + \angle C = 180^\circ

This formula states that the sum of interior angles in any quadrilateral is always 360∘360^\circ. Here, ∠A\angle A, ∠B\angle B, and ∠C\angle C, and ∠D\angle D are the four angles, based on splitting the quadrilateral into two triangles.

∠A+∠B+∠C+∠D=360∘\angle A + \angle B + \angle C + \angle D = 360^\circ

This formula calculates the sum of interior angles for an nn-sided polygon. It is derived from splitting the polygon into (n−2)(n - 2) triangles from one vertex (for a pentagon, 180∘×(5−2)=540∘180^\circ \times (5 - 2) = 540^\circ).

180∘×(n−2)180^\circ \times (n - 2)

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