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Finding angles in isosceles triangles (example 2)

CCSS.Math:

Video transcript

so what do we have here we have a triangle and we know that the length of AC is equal to the length of CB so this is an isosceles triangle we have two of its legs or equal to each other and then they also tell us that this line up here they didn't put another label there let me put another label there just for fun let's call this this is you could even call this array because it's starting at C that line or array CD is parallel to this segment a-b over here and that's interesting then they give us they give us these two angles right over here these adjacent angles they give it to us in terms of X and what I want to do in this video is try to figure out what X is and so given that they told us that this angle that this line and this line are parallel and you could we can turn this into line CD so it's not just array anymore so it just keeps going on and on in both directions the fact they've given us a parallel line tells us that maybe we can use some of what we know about transversals and parallel lines to figure out some of the angles here and you might recognize you might recognize that this right over here this line let me do that in a better color you might recognize that line CB is a transversal for those two parallel lines let me draw both of the parallel lines a little bit more so that you can recognize that as a transversal and then a few things might jump out you have this X plus 10 right over here and it's corresponding angle is right down here this would also be X plus 10 and if this is X plus 10 then you have a vertical angle right over here that would also be X plus 10 or you could say that you have alternate interior angles that would also be congruent either way this base angle is going to be X plus 10 well it's an isosceles triangle so your two base angles are going to be congruent so if this is X plus 10 then this is going to be X plus 10 as well and now we have the three angles of a triangle expressed as as functions of expressed in terms of X so when we take their sum they need to be equal to 180 and then we can actually solve for X so we get 2x 2x plus X plus 10 plus X plus 10 plus X plus 10 plus X plus 10 is going to be equal to 180 degrees then we can add up the exes so we have a 2x there plus an X plus another X that gives us 4 X 4 X's and then we have a plus 10 and another plus 10 so that gives us a plus 20 is equal to 180 and we can subtract 20 from both sides of that and we get 4 X for X is equal to 160 divide both sides by 4 and we get X is equal to 40 and we're done we figured out what X is and then we can actually figure out what these angles are this is X plus 10 then you have 40 plus 10 this right over here is going to be a 50 degree angle this is 2x so 2 times 40 this is an 80 degree angle it doesn't look at it the way I've drawn it and that's why you should never take anything you should never assume anything based on how a diagram is drawn so this right over here is going to be an 80 degree angle and that these two base angles right over here are also going to be are also going to be 50 degrees so you have 50 degrees 50 degrees an 80 they add up to 180 degrees