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

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

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

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

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

1𝑎. 82 𝑜 b. 144 𝑜 c. 75 𝑜 d. 150 𝑜 e. 241 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. 110 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

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.

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.

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.)

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 1800 and 360o Reflex

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