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neurologyYou need to know

• The angles inside any triangle add up to `180^\circ`.
• A polygon is a closed 2D shape made from straight sides.
• The sum of the interior angles of an `n`-sided polygon is `(n-2) \times 180^\circ`.
• A quadrilateral has an interior angle sum of `360^\circ` because it can be split into two triangles.
• 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) \times 180^\circ}{n}`.
• The exterior angles of any polygon, one at each vertex and taken in the same direction, add up to `360^\circ`.
• Each exterior angle of a regular `n`-sided polygon is `\frac{360^\circ}{n}`.
• An interior angle and its adjacent exterior angle in a polygon add up to `180^\circ` because they form a straight line.
• Vertically opposite angles are equal.
• Angles on a straight line add up to `180^\circ`, and angles around a point add up to `360^\circ`.
• When two parallel lines are crossed by a transversal, corresponding angles are equal.
• When two parallel lines are crossed by a transversal, alternate angles are equal.
• When two parallel lines are crossed by a transversal, co-interior angles add up to `180^\circ`.
• An isosceles triangle has two equal sides and the two base angles opposite those equal sides are equal.
• A bearing is an angle measured clockwise from north and is usually written as three digits, such as `047^\circ` or `120^\circ`.
• The bearing of A from B is measured at B, clockwise from the north line through B towards A.
• The angle at the centre of a circle is twice the angle at the circumference when both angles stand on the same arc.
• The angle in a semicircle is `90^\circ`.
• Opposite angles in a cyclic quadrilateral add up to `180^\circ`.

• Calculate a missing angle in a triangle by subtracting the known angles from `180^\circ`.
• Find the interior angle sum of a polygon by substituting the number of sides into `(n-2) \times 180^\circ`.
• Calculate a missing interior angle in an irregular polygon by subtracting the known interior angles from the polygon’s total interior angle sum.
• Calculate each interior or exterior angle of a regular polygon using `\frac{(n-2) \times 180^\circ}{n}` or `\frac{360^\circ}{n}` as appropriate.
• Identify corresponding, alternate and co-interior angles in parallel-line diagrams and give the correct angle reason for each step.
• Solve multi-step angle problems by combining facts about triangles, straight lines, polygons, parallel lines and isosceles triangles, showing reasons for each angle found.
• Draw and measure bearings using a north line, a clockwise angle, and three-digit notation.
• Solve bearing problems by using parallel north lines and angle facts to calculate unknown directions.
• Apply individual circle theorems to calculate missing angles, stating the theorem used for each step.