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neurologyYou need to know

• An interior angle is the angle formed inside a polygon where two adjacent sides meet.
• The interior angles of any triangle add up to 180°.
• A quadrilateral can be split into 2 triangles, so its interior angles add up to 360°.
• A pentagon can be split into 3 triangles, so its interior angles add up to 540°.
• A hexagon can be split into 4 triangles, so its interior angles add up to 720°.
• Any convex `n`-sided polygon can be split into `n-2` triangles by drawing `n-3` diagonals from one vertex.
• The interior angles of a simple concave `n`-sided polygon also add up to `((n-2) \times 180^\circ)`, but drawing diagonals from an arbitrary vertex does not always split it into triangles.
• The sum of the interior angles of an `n`-sided polygon is `((n-2) \times 180^\circ)`.
• The interior angle sum of a polygon depends only on the number of sides, not on whether the polygon is regular or irregular.
• A regular polygon has all sides equal and all interior angles equal.
• Each interior angle of a regular `n`-sided polygon is `\frac{(n-2)\times180^\circ}{n}`.
• If a regular polygon has more sides, each interior angle becomes larger, but for a convex polygon each interior angle is still less than 180°.

• Split a convex polygon into triangles by drawing diagonals from one vertex, and use the number of triangles to justify the interior angle sum.
• Calculate the interior angle sum of any polygon by substituting the number of sides into `((n-2) \times 180^\circ)`.
• Find a missing interior angle in an irregular polygon by working out the total interior angle sum and subtracting the known angles accurately.
• Form and solve an equation for unknown angles in an irregular polygon when more than one angle is missing, using the correct interior angle sum.
• Calculate each interior angle in a regular polygon by dividing the total interior angle sum by the number of sides.
• Check whether an angle answer is sensible by comparing it with the polygon’s total angle sum and, for a regular convex polygon, ensuring each interior angle is less than 180°.