Angles in Polygons & Parallel LinesEdexcel IGCSE Maths: Flashcards

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What do angles on a straight line add up to?

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What do angles on a straight line add up to?: $180^{\circ}$
What do angles around a point add up to?: $360^{\circ}$
What is true of vertically opposite angles?: They are always equal.
What are corresponding angles, and what is their relationship?: Angles in matching positions at each intersection of a transversal with parallel lines ('F' shape); they are equal.
What are alternate angles, and what is their relationship?: Angles on opposite sides of a transversal, between two parallel lines ('Z' shape); they are equal.
What are co-interior (allied) angles, and what is their relationship?: Angles on the same side of a transversal, between two parallel lines ('C' shape); they sum to $180^{\circ}$ .
Formula for the sum of interior angles of a polygon with $n$ sides?: $(n - 2) \times 180^{\circ}$
Formula for one interior angle of a regular polygon?: $\dfrac{(n-2) \times 180^{\circ}}{n}$
What do the exterior angles of any convex polygon sum to?: $360^{\circ}$ , regardless of the number of sides.
Formula for one exterior angle of a regular polygon?: $\dfrac{360^{\circ}}{n}$
Relationship between an interior angle and its exterior angle at the same vertex?: They sum to $180^{\circ}$ (they are supplementary).
How do you find the number of sides of a regular polygon from its exterior angle?: $n = 360^{\circ} \div \text{exterior angle}$
Sum of interior angles of a hexagon ( $n=6$ )?: $(6-2) \times 180^{\circ} = 720^{\circ}$
What condition must hold before applying corresponding/alternate/co-interior angle facts?: The two lines cut by the transversal must be parallel.
One interior angle of a regular pentagon?: $540^{\circ} \div 5 = 108^{\circ}$