Angles in Polygons & Parallel Lines Flashcards

All 29 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 are vertically opposite angles?

The pair of angles opposite each other where two straight lines cross — they are equal.

True or false? When two straight lines cross, two angles next to each other add up to $180^\circ$.

True. They are angles on a straight line.

True or false? If someone measures all the angles around a point and they total $350^\circ$, at least one measurement must be wrong.

True. Angles at a point add up to $360^\circ$.

What are the steps to find a missing angle at a point, with a reason?

e.g. angles of $90^\circ$, $130^\circ$ and $x$ meet at a point

1. Add the known angles: $90 + 130 = 220$
2. Subtract from $360$: $360 - 220 = 140$, so $x = 140^\circ$
3. Reason: angles at a point add up to $360^\circ$

What do the angles in a triangle add up to?

$180^\circ$

What is the size of each angle in an equilateral triangle?

$60^\circ$

What is the angle property of an isosceles triangle?

The two angles opposite the two equal sides are equal.

What are the steps to find the base angles of an isosceles triangle?

e.g. the angle between the two equal sides is $40^\circ$

1. Subtract from $180$: $180 - 40 = 140$
2. Halve it (the two base angles are equal): $140 \div 2 = 70$, so each base angle is $70^\circ$

What is the exterior angle of a triangle equal to?

e.g. the two interior angles at the other two vertices are $50^\circ$ and $60^\circ$

The sum of the two opposite interior angles.
e.g. exterior angle $= 50 + 60 = 110^\circ$

True or false? In an isosceles triangle the equal angles are always the two angles at the bottom of the diagram.

False. The equal angles are the ones opposite the two equal sides, wherever they appear.

What do the angles in a quadrilateral add up to?

$360^\circ$

How many triangles can any quadrilateral be split into, and what does that show about its angle sum?

$2$ triangles, so the angle sum is $2 \times 180 = 360^\circ$.

True or false? A kite's angles add up to less than $360^\circ$ because it is not a rectangle.

False. The angles of any quadrilateral add up to $360^\circ$.

What are the steps to find a missing angle in a quadrilateral, with a reason?

e.g. three angles are $100^\circ$, $80^\circ$ and $90^\circ$

1. Add the known angles: $100 + 80 + 90 = 270$
2. Subtract from $360$: $360 - 270 = 90^\circ$
3. Reason: angles in a quadrilateral add up to $360^\circ$

What are the steps to find an angle outside a quadrilateral, on a straight line through one of its vertices?

e.g. three angles of the quadrilateral are $130^\circ$, $65^\circ$ and $95^\circ$, and the fourth vertex lies on a straight line with the angle $y$

1. Fourth interior angle: $360 - 130 - 65 - 95 = 70^\circ$ (angles in a quadrilateral add up to $360^\circ$)
2. $y = 180 - 70 = 110^\circ$ (angles on a straight line add up to $180^\circ$)

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

What are corresponding angles on parallel lines, and how are they related?

Angles in the same position at each intersection (an "F" shape) — corresponding angles are equal.

What are alternate angles on parallel lines, and how are they related?

Angles on opposite sides of the transversal, both between the parallel lines (a "Z" shape) — alternate angles are equal.

What are co-interior (allied) angles on parallel lines, and how are they related?

Angles on the same side of the transversal, both between the parallel lines (a "C" shape) — they add up to $180^\circ$.

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

False. They add up to $180^\circ$; it is alternate and corresponding angles that are equal.

True or false? Two angles on opposite sides of the transversal and both between the parallel lines are corresponding angles.

False. They are alternate angles.

What are the steps to find an unknown angle on parallel lines and justify it?

e.g. find the angle alternate to a given angle of $65^\circ$

1. Spot the shape: "Z" shape, so the angles are alternate
2. Apply the rule: alternate angles are equal, so the angle is $65^\circ$
3. Write the reason: alternate angles are equal