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 pentagon

$(n-2)\times 180^\circ$

For a pentagon: $(5-2)\times 180^\circ = 540^\circ$

True or false? The exterior angles of a polygon only add up to $360^\circ$ if the polygon is regular.

False. The exterior angles of any convex polygon add up to $360^\circ$, regular or not.

What is the size of each exterior angle of a regular polygon with $n$ sides?

e.g. a regular decagon ($n=10$)

$\dfrac{360^\circ}{n}$

For a regular decagon: $360^\circ \div 10 = 36^\circ$

What are the steps to find the number of sides of a regular polygon from its interior angle?

e.g. interior angle $=150^\circ$

1. Exterior angle $= 180^\circ -$ interior angle: $180 - 150 = 30^\circ$
2. Number of sides $= 360^\circ \div$ exterior angle: $360 \div 30 = 12$
3. So the polygon has $12$ sides.

What are the steps to find missing angles in a polygon when the angles are given in terms of each other?

e.g. a quadrilateral with angles $x$, $2x$, $3x$, $4x$

1. Find the angle sum: $(4-2)\times 180 = 360^\circ$
2. Form an equation: $x+2x+3x+4x = 360$
3. Solve and substitute: $10x = 360$, so $x = 36^\circ$ and the angles are $36^\circ, 72^\circ, 108^\circ, 144^\circ$.

What are the steps to find the angles in the triangle made by two sides of a regular polygon and the diagonal joining their ends?

e.g. a regular hexagon

1. Find the interior angle: $((6-2)\times 180)\div 6 = 120^\circ$
2. The triangle is isosceles (two equal sides), so the other two angles are equal.
3. Each base angle $= (180 - 120)\div 2 = 30^\circ$