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- Glide: 1
- Hello my name is Mark, and I am a mathematician, Today I am going to be testing out how geometry and angles are used in the real world! Im going to call some of my friends to see how they use it and help them solve their issues.
- It looks like Im getting a call from my buddy that works in construction. He needs help calculating angles in parallel lines for the new roads he is making. Lets drive over there and help.
- Glide: 2
- Hey Jack, I can definitely help. First we find whats given which is 54 degrees for angle 2 and angle 3 and 1 being 126. To find angle 4 we can use the exterior angle theorem. First we know that angle 2 and 1 are supplementary as they are a linear pair. Angle 2 plus angle 1 are 180 and angle 2 + angle 3 is 180 as it makes a straight line. This means angle 1 and 3 are equal. and angle 3 and 4 are also linear pairs so they also equal 180 so angle 2 + angle 3 is 180 and angle 3 plus angle 4 is 180. So if we do substitution of equality we get angle 2 + angle 3 is = to angle 3 + angle 4. So we do subtraction of equality and remove angle 3 and get angle 2 is equal to angle 4 therefor angle 4 is 54 degrees making it safe and legal.
- Hello Mark, I am trying to build a road through these 2 parallel roads where the line is so that people can switch the road they are going on. I will also build traffic lights at the white spaces between the roads so that cars do not collide. The issue is that to do this i must calculate the missing angle to test if its safe for a car to turn at, it must be at least 50 degrees to be safe and legal. Can you help me?
- angle 3: 126 degrees
- angle 4: ?
- angle 2: 54 degrees
- angle 1: 126 degrees
- Glide: 3
- You are very welcome let me know if you need help with anything else in the future good bye!
- Thank you so much Mark for teaching the alternate interior angle theorem and helping me learn how to find angles in parallel lines. We will definitely start making this road and we thank you for all your efforts and help.
- Glide: 4
- That was really fun now we are going to my other buddy Jamies lab to help him build robots, by finding interior and exterior angles.
- Glide: 5
- Hi Mark, how are you? I am building a robot and am having a lot of trouble with making the connecting bit of the arm the right shape to run my code. It has to be a regular polygon with interior angle measurement of 108, what shape would that be?
- Ok Jamie let’s figure this out. The formula for this is 180 x n-2 divided by n = 108 (n being the number of sides of the shape). We start by multiplying both equations by n making it 180 x n-2 = 108. Next we expand making it 180n-360 = 108n, after that we transfer the -360 to remove the negative making the current equation 180n = 108n + 360. next we minus 108n from both sides to have n on only one side. This makes it 72n=360 so we divide both by 72 and get n=5.
- Glide: 6
- We can now check our answer by doing 180 x n-2 divided by n. Which is 180 x 3 since 5 is n and 5-2 is 3. 180 x 3 is 540 and 540 divided by 5 is 108. Which means it is a 5 sided polygon which is a pentagon so you have to use a pentagon.
- Ok thank you I will make sure to use a regular polygon in the shape of a pentagon the next time I try.
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