The four angles come to 360°
You measure all four corners of three different tiles. Every total comes out the same. Why?
- A quadrilateral, four corners.
- A diagonal joins two corners that are not neighbours. It splits the shape into 2 triangles.
- Each triangle's angles total 180°.
- 180 + 180 = 360°.
Each tile splits into two triangles. Each has 180°, so the tile has 360°.
Rule: A diagonal inside the shape cuts it into two triangles. Each totals 180°. So the four angles of a quadrilateral always total exactly 360°.
Three corners of a shape measure 100°, 80° and 90°. Together they make 100 + 80 + 90 = 270°. The fourth corner is 360 − 270, which is 90°.
Push one corner inwards and the shape is dented. That corner is now more than 180° — a reflex angle. The total is still 360°. Corners of 90°, 30°, 210° and 30° add to exactly 360°. In a dented shape, use the diagonal from the dented corner. That diagonal lies inside the shape.
Drag the slider to push corner D in. Watch the total.
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