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Measuring angles

Basic shapes

Japanese school year: Elementary 4

What you learn

Learn the unit of degrees and how to measure and construct various angles using a protractor. Understanding angles is useful in navigation, astronomy, and observing slopes or hands on a clock. Prior familiarity with right angles, vertices, and straight lines will help you read protractor scales accurately and comfortably.

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Key points

This formula shows the angle sum of a triangle. Adding all three inside angles (A, B, C) always equals 180°.

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

This formula shows the angle sum of a quadrilateral. Adding all four inside angles (A, B, C, D) always equals 360°.

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

This formula finds the angle sum S of a polygon. Subtract 2 from the number of sides n, then multiply by 180°.

S=180∘×(n−2)(n≥3)S = 180^\circ \times (n - 2) \quad (n \ge 3)

This equation shows the rule for intersecting lines. The opposite angles a and b are always the exact same size.

∠a=∠b\angle a = \angle b

Choose a set to practice.