Find unknown angles in triangles, quadrilaterals, and regular polygons using angle sum properties
You already know how to classify shapes by their sides and angles, and that angles come in different sizes. Now you can use angles as clues to solve puzzles. Every triangle's three angles add up to exactly 180°. If you know two of them, you can find the third one without measuring anything.
Two angles in a triangle are 55° and 70°. Add them: 55° + 70° = 125°. Then subtract from 180°: 180° - 125° = 55°. The third angle is 55°.
A quadrilateral's four angles always add up to 360°. You can see why by splitting it into two triangles: 180° + 180° = 360°. Regular polygons with more sides follow the same pattern. A regular hexagon has six equal angles that add up to 720° in total.
To find one angle in a regular polygon, divide the total angle sum by the number of angles. For a regular hexagon: 720° ÷ 6 = 120° for each angle.
Add up the angles you already know, subtract from the shape's total, and what's left is the missing angle.
You have found missing angles from totals: 180 on a line, 360 around a point. Every triangle hides its own total too: its three corners always add up to exactly 180°. A triangular flag has corners of 55° and 70°.
What is the flag's third corner?
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12 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.