Angles in Polygons & Parallel Lines Flashcards

All 18 cards in this deck

What do angles at a point add up to?

$360^\circ$

What do angles at a point on a straight line add up to?

$180^\circ$

What is true about vertically opposite angles?

They are equal.

e.g. two lines crossing with one angle $50^\circ$ give $50^\circ$ opposite it.

What do the angles in a triangle add up to?

$180^\circ$

What is the exterior angle of a triangle equal to?

The sum of the two opposite interior angles.

e.g. interior angles $40^\circ$ and $70^\circ$ give an exterior angle of $110^\circ$.

In an isosceles triangle, what do you know about the angles?

The two base angles (opposite the two equal sides) are equal.

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 $= (180 - 120)\div 2 = 30^\circ$

What is true about corresponding angles on parallel lines?

They are equal.

They are in the same position at each parallel line (an "F" shape).

What is true about alternate angles on parallel lines?

They are equal.

They lie on opposite sides of the transversal, between the parallel lines (a "Z" shape).

What is true about co-interior angles on parallel lines?

They add up to $180^\circ$.

e.g. if one is $110^\circ$, the other is $70^\circ$.

True or false? Co-interior angles on parallel lines are equal.

False. Co-interior angles sum to $180^\circ$; it is alternate and corresponding angles that are equal.

True or false? Alternate and corresponding angle facts only hold when the two lines crossed by the transversal are parallel.

True. Without parallel lines these angles need not be equal.

In a question saying "give a reason for each stage of your working", what must you write next to each angle you find?

The angle fact used, in standard wording.

e.g. "alternate angles are equal", "angles on a straight line sum to $180^\circ$", "angles in a triangle sum to $180^\circ$".