5.4 Practice A Answers

I divided it by 8 equal angles, because in the directions, it says it's a regular polygon. These are regular. So I can share equally. Once I know the exterior angle is 45, I'm using the fact that the interior angles and the exterior angles add up to one 80. So if I know the exterior angles 45, plus whatever the interior angle is, has to equal one 80. I'm just finding this missing amount I subtract 45 on both sides I get one 35. I showed that in my PowerPoint, I'm going to bring it up for you so you can see it. Right here we talked about that. Number four asks to find the sum of the interior angles. Of a hexagon. So the sum, we talked about that in the PowerPoint as well. To find the sum of your angles you use the formula N minus two times one 80. When I ask you to show me work ladies and gentlemen, I don't need you to show me the multiplication and division and adding and subtracting. That's elementary schoolwork. You can do that on your calculator. In fact, I want you to check your work on your calculator. 

Work in pre algebra means show me what rule you used, what equation you're using. This is the rule for interior angle sum. Show me the next step is you're plugging the information in. N stands for the number of sides, so since we're talking about a hexagon, there are 6 sides, we're taking away two, and then eventually multiplying by one 80. And then we get four times one 80. So the sum was 7 20 for number four. 6, 6, set to find the measure of an exterior angle of a regular Pentagon. Again, because it's regular, we can just take that sum of exterior angles, which is all day every day, 360. The sum of the interiors you have to find do a little work for. But the exterior angles you just plug in that 360. We can share it equally because it's a regular polygon and they each equals 72°. Number 8, a lot of people took 360 and divided it by three. You can not do that for number 8 because as you see in the picture, all the interior angles are not the same, so it's not regular. We're finding these exterior angles here. Very similar to this problem once again. So I show you the rule that I use is I know the interior plus the X here equal one 80 because they're supplementary. 

I plug in what we know about vertex a we know the interior angles 37. I don't know the exterior angle. We're subtracting 37 from both sides. And then you do that for every single angle. B and I actually forgot to label this C. All right, where should we go next? Number ten, they're just asking for the sum of the interior angles so we're using this formula again. It's a Pentagon, so you're using 5 sides, which means there's three triangles, and the sum would be 540 of all the angles inside. 12, 12 is asking for an exterior angle of this shape, which is obviously not regular. That's what it looks like. Again, you can see all the exterior angles are not the same, so it's not a regular shape. So what we do know is that all of those angles always equal 360. So we're going to add up all those exterior angles to equal 360. Very similar to the PowerPoint slide that I showed you. Let's find it. Here. This problem is exactly like that problem. Except you have different angles. So especially when you're working at home now, you really have to master the skill of seeing how I do one example and you making your problem look exactly like that. 

Finally, we're at 14, we're finding one interior angle. And I know that when 14 a says to find the measure of angle a which is interior, I know some of you may not have been able to see it because it was dark, but this is a hexagon. We would need to know the sum of all the angles and then we can share it because it's a regular hexagon equally between the 6 angles. Well, the sum is 720. I know that and I'm not going to do my work for that because we already found this sum up here of a hexagon. On the same page, so there's no point of doing the work twice for that. So I use that sum of 7 20, I shared equally between the 6 sides, so the interior angle, notice how I have the interior angle. So this is how neat nice and neat my work looks. It's 120. And then I use the fact up here. Interior plus X tier supplementary, so I just know that if I already have one 20 inside, 60 has to be the exterior because they're supplementary. They add up to one 80. And there you have it. I hope you listened. I hope you figured out what you did wrong. I'm gonna be posting another video about the review. See you later, guys.