1. Slideshow 36, Mathematics Mr Richard Sasaki, Room 307
Angles and Lines
Slideshow 36, Mathematics
Mr Richard Sasaki, Room 307

2. Objectives Review angle properties learned so far
Understand alternate angles
Calculate missing angles at certain points

3. Angle Properties
Let’s have a look back at what we have learned so far.
A polygon with n sides has a sum of interior angles ___________.
180(n-2)o
Any polygon has sum of exterior angles ________.
360o
At a point, a polygon’s interior and exterior angle add up to ________.
180o

4. Angle Properties A right-angle is exactly _______. 90o
On an Equilateral triangle, each angle is ______.
60o
On two straight lines, opposite angles are always ________.
equal

5. Angle Properties Try the first worksheet!
A pair of parallel lines have two corresponding angles between them that add up to _______. 𝑥
180 𝑜 −𝑥
180o
360 𝑜 −𝑥
All angles around a point add up to _______. 𝑥
360o

6. 1𝑎. 82 𝑜
b 𝑜
c. 75 𝑜
d 𝑜
e 𝑜
f. 80 𝑜
2. 𝑎, 𝑐, 𝑒, 𝑔, 𝑖, 𝑘, 𝑚, 𝑜
𝑎𝑟𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒
𝑏, 𝑑, 𝑓, ℎ, 𝑗, 𝑙, 𝑛, 𝑝
Answers
1𝑎 𝑜
b. 95 𝑜
c. 40 𝑜
d. 13 𝑜
e. 32 𝑜
f. 46 𝑜
2. 72o
3. 𝑎= 152 𝑜 , 𝑏= 28 𝑜 , 𝑐= 152 0

7. Alternate Angles
You should have found out from the last question on the worksheet that o and e are the same size. e o
These are called alternate angles and are shaped in like a “Z” format where the top and bottom lines are parallel.

8. Naming Lines and Angles
Lines are often labelled and this gives the ability to name angles. E A B 𝑥
Angle 𝑥 can be known as ∠AEF or ∠FEA. C D F
Here we can see lines AB, CD and EF. (Note: Line AB and BA are the same.)
Lines are of infinite length. Lines that aren’t are called line segments.

9. Line Segments Let’s try the Activote exercise.
Shapes are usually made of line segments. A B
Here, AB, AC, CD and BD are line segments. C D
Which two line segments are parallel?
AB and CD
We can denote this as AB ∥ CD.
(“∥” means parallel.)

10. Acute, Obtuse or Reflex? Try the final worksheet! Between 00 and 90o
We know that a right-angle is 90o, there is 180o on a line and 360o around a point but how about in between?
Between 00 and 90o
Acute
Between 900 and 180o
Obtuse
Between and 360o
Reflex

11. Answers Acute, obtuse, right-angle Acute, straight, reflex
Reflex, acute, right-angle
2. Reflex
3. It must be acute, a right angle or obtuse
4. 4
5. AB ∥ CD, ∠CAB (or ∠BAC)
6. Line, line segment