Angle facts, parallel lines and polygons
Angle facts
- These are valid reasons in the exam — learn the words.
- Angles at a point add up to $360^{\circ}$.
- Angles on a straight line add up to $180^{\circ}$.
- Vertically opposite angles (where two lines cross) are equal.
- Worked example: $x + 50 + 70 = 180$ on a line → $x = 60^{\circ}$.
Practice
Three angles on a straight line are x, 50° and 70°. Find x (degrees).
x + 50 + 70 = 180, so x = 60°.
Angles in parallel lines
- When a line crosses two parallel lines:
- Corresponding angles (an "F" shape) are equal.
- Alternate angles (a "Z" shape) are equal.
- Co-interior angles (a "C" shape) add up to $180^{\circ}$.
- Worked example: a co-interior angle to $110^{\circ}$ is $180 - 110 = 70^{\circ}$.
Practice
A co-interior angle to 110° (between parallel lines) is how many degrees?
Co-interior angles add to 180°: 180 − 110 = 70°.
Polygons
- For a polygon with $n$ sides:
$$\text{interior angles sum} = (n-2)\times 180^{\circ}, \qquad \text{exterior angles sum} = 360^{\circ}$$
- A regular polygon has all sides and angles equal.
- Worked example: a regular hexagon — exterior $= \tfrac{360}{6} = 60^{\circ}$, so interior $= 180 - 60 = 120^{\circ}$.
Practice
Each interior angle of a regular hexagon is how many degrees?
Exterior = 360/6 = 60°, so interior = 180 − 60 = 120°.
Practice
The interior angles of a pentagon (5 sides) add up to how many degrees?
(n − 2) × 180 = (5 − 2) × 180 = 540°.
You've got it
Key idea
- at a point $360^{\circ}$; on a line $180^{\circ}$; vertically opposite are equal
- parallel lines: corresponding (F) equal, alternate (Z) equal, co-interior (C) add to $180^{\circ}$
- polygon: interior sum $(n-2)\times 180^{\circ}$, exterior sum $360^{\circ}$