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neurologyYou need to know

• The angles in a triangle add up to `180^\circ`.
• A polygon with `n` sides can be split from one vertex into `n-2` triangles.
• The sum of the interior angles of an `n`-sided polygon is `(n-2) \times 180^\circ`.
• The exterior angles of any convex polygon add up to `360^\circ`, one at each vertex.
• In a regular polygon, all sides are equal and all interior angles are equal.
• Each interior angle of a regular `n`-sided polygon is `\frac{(n-2) \times 180^\circ}{n}`.
• 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.
• Corresponding angles in parallel lines are equal.
• Alternate angles in parallel lines are equal.
• Co-interior angles in parallel lines add up to `180^\circ`.
• Vertically opposite angles are equal.
• The base angles of an isosceles triangle are equal.
• Bearings are measured clockwise from north and are written as three figures, such as `047^\circ` or `120^\circ`.
• The angle at the centre of a circle is twice the angle at the circumference when both angles stand on the same arc.
• Angles at the circumference in the same segment of a circle are equal.
• The angle in a semicircle is `90^\circ`.
• Opposite angles in a cyclic quadrilateral add up to `180^\circ`.
• The radius of a circle meets a tangent at `90^\circ` at the point of contact.
• The angle between a tangent and a chord is equal to the angle in the alternate segment.

• Deduce the interior angle sum of a polygon by splitting it into triangles and using `(n-2) \times 180^\circ`.
• Find missing angles in irregular polygons by combining the polygon angle sum with straight-line, full-turn and vertically opposite angle facts.
• Calculate each interior angle of a regular polygon using `\frac{(n-2) \times 180^\circ}{n}` and state the answer in degrees.
• Calculate each exterior angle of a regular polygon using `\frac{360^\circ}{n}` and use interior plus exterior equals `180^\circ` when needed.
• Identify and label corresponding, alternate and co-interior angles in parallel lines, giving a correct reason for each angle found.
• Solve multi-step angle problems by selecting and linking facts about triangles, isosceles triangles, polygons, parallel lines and angles around points.
• Draw and interpret bearings by measuring clockwise from north, using three-figure notation and accurate angle construction.
• Apply individual circle theorems to find missing angles, giving the theorem as the reason.
• Combine several circle theorems with other angle facts to solve multi-step circle geometry problems.
• Use algebra in circle theorem problems by forming equations from angle relationships, solving for the unknown, and substituting back to find required angles.