Angles in Polygons Flashcards

All 6 cards in this deck

What is the formula for the sum of the interior angles of a polygon with $n$ sides?

e.g. a hexagon

$(n - 2) \times 180^\circ$
e.g. $(6 - 2) \times 180 = 720^\circ$

What are the steps to find a missing interior angle of a polygon?

e.g. a pentagon with angles $100^\circ$, $110^\circ$, $120^\circ$, $130^\circ$ and $x$

1. Angle sum: $(5 - 2) \times 180 = 540^\circ$
2. Add the known angles: $100 + 110 + 120 + 130 = 460$
3. Subtract: $540 - 460 = 80$, so $x = 80^\circ$

What do the exterior angles of any polygon add up to?

$360^\circ$

How is the exterior angle of a regular polygon linked to its number of sides?

exterior angle $= 360^\circ \div n$, so $n = 360^\circ \div$ exterior angle.
e.g. exterior angle $15^\circ$ gives $360 \div 15 = 24$ sides.

How do you find an interior angle of a regular polygon from its exterior angle?

e.g. a regular pentagon

interior angle $= 180^\circ -$ exterior angle.
e.g. $360 \div 5 = 72$, so interior angle $= 180 - 72 = 108^\circ$

True or false? The interior angles of a decagon (10 sides) add up to $10 \times 180^\circ$.

False. It is $(10 - 2) \times 180 = 1440^\circ$.