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Section 6.1 Video

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Video of the section 6.1 lesson being taught by me.

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cancer today we're going to start on chapter 6 or look at section of chapter 6 section 1 if you have it already when you quiz if you will come up to where the bands are at grab your chapter 6 notes and remember this test on Friday to the next unit will be The Last Unicorn day before Christmas so if you would if you had already gotten the notes go ahead and do come up here and get those I do also remember tomorrow we will have our Section 5 6 and that will be Daddy I will be here for tutoring in the morning for the rest of this week and also one more thing for tomorrow do you remember your schoology login stuff if you need to email me tonight to get your email for your login information and make sure you can log in before tomorrow is going to make what we're going to do tomorrow at the lot quicker and a lot more simple for you so so far we've been talking a lot about triangles we're going to move into another type of polygon with three quadrilaterals are four-sided figures so the first section were really just going to discuss any types of angles within polygons and it's actually includes quadrilaterals really any type of polygon so this section is not just limited to quadrilaterals like the rest of the chapter unit will be this section is actually going to represent angles of all types of polygons we're going to talk about the interior angle exterior angles of all types of polygons have a couple different formulas that were going to be using your the first one of the interior angle sum and what that says is take 180 degrees and we multiply that by in -1 and represents the number of sides of the polygon to every polygon can be broken in two triangles so obviously if you have a triangle that's one triangle 83 sides - 100 B 3-1 so that's why it's a hundred eighty degrees where is a quadrilateral is a four-sided figure so India would represent for so that would be 180 4-2 so that would be 180 * 2 would be 360 degree so 360° will we what all quadrilaterals four-sided figures that up to and so a quadrilateral a four-sided figure can be broken into two try so in modest to the number of sides -2 that tells you how many triangles the figure can be broken into so if it was a you know 20 sided figure that means it could be broken in if it is the interior angle measure then can be by taking the sum of 80 and -2 biting buy it now this would only be if it is a regular figure between all the sides and all the angles are equal regular figures in the past the exterior angle represented by taking 360 degree and dividing by aunt which is the number of thought so this would be for any figure doesn't matter what it is now the reason it's 360 here is because all figures are inscribed within a circle circles are 360° so that's where the 360 come so the 180 comes from the fact that in mind as to represent the number of triangles within any figure 180 is a triangle measures that's how we get this measurement 360 comes from the fact that I Circle surrounds or circumscribe any figure so we take that Farkle 360 divided by the number of sides and we can figure what the angles are exterior of a figure don't forget some examples here and I'm going to kind of go through some of these give you a few minutes to kind of look at these yourself and sometimes dad were going to give you a homework sheet that you can work on this section with your groups or you can also decide to work on your you can also decide work on your study guide for test on Friday if you would rather but both of these things have to be done it's really kind of your choice up to you so we measure of the sum of the interior angles of a convex nonagon alright so convex nonagon nonagon Rivers 9 sides so that means remember when typing a little bit bigger here so you can see it that means we're going to use the 180 and modest too formula to find the interior angle sum now the fact that it's stop that we don't / and we just want to know what is the total of an entire Donna God's let's 9-2 so that's 180 * 7 which would be 1200 and 60 degrees do you make sure you put your degree symbol this program I just can't put a little degree symbol here but do make sure that you did put that so there is 1260 in every naughty nonagon so that means that there are 7 triangles and -2 within a nonagon I don't think the number to know this is a quadrilateral how to find out what is the measure of X and then what is the measure of each angle here first we need to figure out we can stay obviously that this quadrilateral is not a regular figure all four sides are definitely not the same there's no way that tea and answer actually the same later on in the chapter are we going to talk about this would be considered a parallelogram is it says in the directions there but so all the sides are not thoroughly equal there so we can just fit each of the interior angle we need to figure out what that song is so we're going to take 180 4-2 which is 80 x two triangles are 360 as we discussed in the past you may have already known that and didn't necessarily have to do this portion right here for the next thing we're going to do is add up all the sides or into 11 x + 4 plus 5X plus another 11 x + 4 plus that final 5 x 2 equal 360 right so we do that so we can find at X hear that it's going to equal 11 but the problem that if I find egg the problem says find the measure of each interior angle greater than the measure of angle X and remember I can't do it on this program but you write the little angle symbol S in Savannah right all of that out it's going to be 11 * 11 + 4 + 121 + 4 is 125 degrees the measure of angle you Lowe's on 225 degrees the measure of angle T is fine * 11 * 55 and the measure of angle r is awesome 55° finally just to make sure you're correct the last little thing you'd want to do is add up all four of these and do make sure he comes up to me 360° what's going to look at problem never too so that the last ones we were looking at the sum of the interior angles in this one we're going to be looking at each interior angle it says the miles is on so that Bob walkways made it a 3/4 in the shape of a regular pentagon Donna measure of one of the interior angles of a pentagon so this one says it's a regular Pig remember it's only worth the interior angle finding each interior angle only two words if it's a regular picture and it says regular pentagon pentagon so we're going to use the equation 180 you're not it's too and then divide that entire thing. In it's going to be 180 in Disguise Anna's 5-2 worried about all of that by 5 so 180 * 3 / there's three triangles here / thought the 180 * 3 is going to be 500 40 we divide that by 5 we see that each interior angle equals 108 degrees 4 degrees symbols that you have your units for each measure so let me see what you look at this one a second and see if you can kind of figure this out before I go over to the measure of an interior angle of a regular polygon is 150 degrees find the number of sides of the polygon I remember the last one we just did this one was the angle equals 180 in - 2 / in represent the number of sides here we know it's a regular figure so we know that we can use this right here but it's asking is for n it's not asking us for the angle it's asking for and they gave the angle so they gave us this they're looking for in so let me see if you can figure this one out before we go together let me let you talk with your groups for about 2 minutes on there so what kind of talk about that in this case we know the 150 equal to the formula 180 in - 2 / in that we just use I'm going to actually write this a little bit different I'm going to put the N down here which is real see how I would have been riding at the whole time if I didn't have to type it out and I'll put that nail bar over it like that now I can use a couple of different things here to me I think that you do think it's going to get that the end out of the denominator I'm going to multiply both sides of death let me do it a different color so you can say I'm going to multiply both sides of there by 10 to get it out of that denominator so that what I have here now is 150 and 180 yeah and -2 then I can again you can do a couple of different things would I think it would be best maybe is if you go ahead and distribute the 180 to get a 180 n - 360 I need to get the ends on the same side so I subtract 150 - 180 in and I get a -30 in equals a negative 360 double negative there then I divided by -30 so and was 12 and at 12 is representing that there are 12 sides in the figure could be a decagon there's 12 are all equal in the figure Blues couple examples we're going to have is going to do the exterior angle so you can see all the dates figure all of this figure here there is one tooth 7 sides it doesn't really matter the number of sides but we do see that they're not necessarily congruent to each other so we can't use our exterior angle sum hear that 360 way / end because if not a regular big you're here but we can do is we can stop for eggs because we know the measure of each angle so we can add up all the 5X minus 6 5 X -5 4x + 3 okay thanks 12 2x + 3 + 5 x + 5 to equal that in tiresome 360° so weak all of those are together to equal that thumb what are we at all of those X's we end up getting 31 x Plus excuse me - 12 DayQuil 360 so I get this 31 x equals 3/7 so ask then is going to equal $0.12 offer X so we could plug them back in if we want to know each individual angle but she would say that they're definitely not going to be the same friends The Bangles going to be 60 where is this angle is going to be 42 and so on so on so we could to make sure there are algebra was right here plug-in see what they all are and the double check by adding it up and they should equal 360 so if it's not a regular figure you. Check the measure of each angle like we did in problem number one day that parallelogram added up to the someone exterior situation at all I did 360 I'm in an inch your situation they had two different things example we did was in a parallelogram with the interior so I decided to 360 but hadn't been a triangle would have been 180 at it been a pentagon it would be 5:40 and so on so on so on but don't worry we have one word answers to find the measure of each exterior angle of a regular decagon decagon sides so in this case it's a regular decagon that means all the sides are equal so we take it some 360 / in so 360 / 10 is going to be that it's numb in 36 degree so I know what you're going to do is your going to get your homework sheet and you can work with your group on this homework or on your study guide for your test on Friday you have both things we working on to have plenty to work on for the rest of class I'll see you guys too

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