Missing angles (CA geometry)

we're on problem 46 in the figure below line segment a-b is parallel to see see I think there's a typo here I've got to believe this is going to be seedy that's got to be a typo alright so a B I'm assuming is parallel to CD that's probably what they wanted to have because you can't be parallel to a vertex alright and they say what is the value of X so the way to think about it is let's you know if these two are parallel lines then this segment up here is a transversal right if we just extend the two lines like this let me see if I can do it well so if I extended that line like that and if I extended this line like that then segment ad is just a transversal let me see if I can do that one right so if I just extended it like that you see it's a transversal I can go the other direction as well I think you get the idea so if that is a transversal what do you know about transversal we know we know that let's see X plus this angle right here this I'll draw it small is congruent to this angle or over here so the measure of this angle is also X plus 40 right because they're corresponding angles and you can see that by inspection and if you moved around the transversal it makes sense that that's the case so this is X plus 40 and this is X minus 40 and they're clearly supplements of each other they're supplementary angles then the sum of these two angles have to be equal to 180 so let's figure it out so X minus 40 plus X plus 40 is equal to 180 because they're supplementary let's see the 40's cancel out so you just minus 40 plus 40 adds up to zero so we're left with 2x is equal to 180 X is equal to 90 so it's D D 47 the measures of the interior angles of a Pentagon are okay they give us 2 X 6 X 4 X minus 6 2 X minus 16 and 6 X plus 2 what is the measure in degrees of the largest angle okay so first of all we have to remember what is the sum of the interior angles of a pentagon and that's where I always I just draw an arbitrary Pentagon let me see if I can do that let me see actually there's a polygon tool here so let me see how does it work c1 so I'm just trying to draw a pentagon three four five I don't know if that's any different than the line tool but regardless so how many triangles can I draw on a pentagon that tells me what my total interior angles are and there is a formula for that but I like relying on your reasoning more than the formula because you might forget the formula or even worse you might remember it but not have the confidence to use it or you might remember it wrong ten years in the future so the best thing to do is if you have a polygon just count the triangles in it straightforward enough it's almost easier than using the formula so Pentagon has three triangles in it so the sum of its interior angles are going to be three are going to be so the sum of all of the angles are going to be three times 180 right because it's three triangles in it and each triangle has 180 degrees I know you can't see what I just wrote right so the sum of all of these angles are going to be the sum of all of the angles and all in all three triangles so three times 180 is equal to 540 degrees so that's the sum of all of these interior angles now they say that each of them are you know 2 X 6 X etc so the sum of all of these terms have to be equal to 540 so we could write I'm going to write them vertically it makes them easier to add so if we write there 2 X 6 X 4 X minus 6 2 X minus 16 and 6 X plus 2 6 X plus 2 this is going to be the largest right that sum is going to equal 5 for you so let's add this up minus 6 minus 16 that's minus 22 plus 2 is minus 20 all right that's right yeah because we have my yep minus 4 a minus 20 and then have 2 X plus 6 x that is 8 X plus 4 is 12 12 plus 2 is 14 14 plus six is 20 so we have 20 X minus 20 is equal to 540 degrees I know you can't see that 500 let me write it again 20 X minus 20 is equal to 540 let's divide both sides of this equation by 20 so you get X minus 1 is equal to let's see 54 divided by to be 54 divided by 2 which is equal to 27 so then X is equal to add 1 to both sides X is equal to 28 and they want to know what is the measured degrees of the largest angle that's going to be this one right that's the largest one it's 6 times X plus 2 so 6 times 28 what's 28 times 6 it's 48 2 times 6 is 12 plus 4 is 168 so it's 168 plus 2 so plus 2 it's 170 degrees choice C problem 48 what is the measure of angle 1 the measure of angle 1 so this we're going into the angle game and these are fun because they're kind of these deductive reasoning problems where you just use a couple of simple rules and just fill it the whole thing so let's think about it this is 36 degrees they tell us that this whole angle right here is a right angle so what this angle right here is going to be the complement to 36 degrees right 36 Plus this angle have to be equal to 90 so what's this one this one is 90 minus 36 which is what 54 right that's going to be 54 degrees 90 minus 30 is 60 right this 54 and now this angle right here that's going to be the supplement of 88 so this is going to be I'll do it in a different color 180 minus 88 that is equal to 92 degrees now this angle 1 plus the 54 plus the 92 is equal to 180 so we know that you know measure let's say angle 1 plus 54 plus 92 is equal to 180 so angle 1 let's see 54 plus 92 96 this is 146 is that right 146 I think is equal to 180 subtract 146 from both sides the measure of angle 1 is equal to let's see 80 minus 40 80 minus 40 is 40 so 80 minus 46 is equal to 34 degrees so the answer is a problem 49 what is the measure of angle w-z X so they want to know what this angle right here is so let's let's do the angle game some more let's see we can immediately figure out what this angle is because it is the supplement of 132 degrees so this is going to be 180 minus 132 and that's what 80 minus 30 to 80 minus 30 is 50 minus 2 is so this is 48 degrees so this is 48 this angle Plus this angle is going to be equal to this angle all right so this angle or this angle Plus this angle Plus this angle is equal to 180 I don't know what I just said I think I said something wrong so the sum of that so these let's say write that down so this angle is going to be equal to 180 minus 52 minus 48 because the sum of the truck angles add up to 180 and so that is equal to 180 minus let's see let's see that's minus 100 all right which equals 80 degrees so this angle right here is equal to 80 degrees and the angle they want us to figure out is the opposite of this angle or in the US I guess they say vertical angles so this is and so opposite or vertical angles are equal or they're congruent so this is going to be 80 degrees as well and that is choice a problem 50 what is the measure of an exterior angle of a regular hexagon so a regular hexagon tells us that all the sides are the same it's equilateral and all of the angles are the same equiangular so if we just knew how many what's the total degree measure of the interior angles we could just divide that by six and then that would give us what the each of the interior angles are and then we could use that information to figure out the exterior angle so let's just do it so once again I like to just draw a hexagon let's just draw a hexagon and count the triangles in it two sides three sides four sides five sides and six sides and how many triangles do I have here see I could draw one length one two three so I have one two three four triangles so the interior the measure the sum of the interior angles of this hexagon of any hexagon whether it's regular or not are going to be four times 180 and that's equal to what that's equal to 720 180 times two is 360 right that's equal to 720 degrees and it is a regular hexagon so all the interior angles are going to be the same so and there are six of them so each of them are going to be 720 divided by six 720 goes into well six goes into 72 twelve times right so each of the angles of this regular hexagon record each of the interior angles are going to be 120 degrees then I didn't draw it that regular but we can assume that all of these are each 120 degrees fair enough now if all of those are each 120 degrees what is the measure of an exterior angle well we could just extend one of these sides out a little bit now we could say okay if this is 120 degrees what is its supplement well these have to add up to 180 so 180 minus 120 is 60 degrees right I can do it on any side I could extend that line out there and say oh that's 60 degrees so any of the exterior angles are 60 degrees B all right let's see do I have time for one while wait for the next one the next video see you soon