Parallel Lines and Transversals Geometry SpokenMath

today in geometry class we're going to learn how to solve for given parallel lines and transversals this is what we do let's look at question 19. notice this angle and this right angle they're called alternate exterior angles and they're always equal to each other so if we say 21x plus 6 equals 90 degrees we're able to solve for so we're going to subtract 6 from both sides those two go away we get 21x equals 84 degrees now we need to divide both sides by 21 and we'll get the equals 4. so for number 19 equals 4. let's try number 20. this degree and this degree are called corresponding angles and again those are congruent to each other so we can set them equal to each other 75 equals 11x minus 2. let's add 2 to both sides you always want it to equal 0 so we can cancel it out so we have 11x equals 77. divide both sides by 11. again the elevens will cross out we have equals seven as our next answer now let's look at question 21. so 60 degree angle and 8x minus four angle those are considered alternate interior angles again those two are equal to each other so we can just set the equations equal to each other let's add 4 to both sides they cancel each other out we have 8x equals 64. and then divide by 8 to get by itself so we have equals 8. all right that's our answer for 21. let's try 22. we are given these two angles again very similar to question 21 they're called alternate interior interior angles and they are equal to each other so let's set them equal okay let's subtract 139 from both sides that goes away so equals negative seven and this is okay because this is just the value of our now if our angle was equal to negative then something would be wrong let's continue to 23. so these two angles are called alternate exterior angles and those are congruent again set them equal to each other to solve for okay so have numbers on the left and right side as well as x's on my left and right it depends on what you want am just going to subtract 12x from both sides so 14x minus 12x is 2x equals and let's get rid of that negative one so i'm gonna add one to both sides so the ones will cancel each other out seventeen plus one is eighteen divide both sides by two the twos will cancel out so equals nine the last question twenty-four this angle and this angle are corresponding angles again corresponding angles are equal to each other so we can set them equal to each other to solve for i'm going to move the 21x over to the other side they cancel out 23x minus 21x is 2x equals now need to move the 5 over so i'm gonna add five to both sides those two cancel so we have five plus five gives us ten divide by two to both sides they cancel each other out equals five so that's how you can solve for given the type of angles that you're given now for problems 25 to 28 the directions say find the measure of the angle indicated in bold so in this prop these problems you don't want to solve for you want to solve for the actual ink for question 25 these two angles are called consecutive interior angles these are the only two angles that will add up to 180 so if we add them up the equal to 180 see how that we have two of the same so just add plus gives us 2x 96 plus 96 gives us 192 and that equals 180. so let's subtract 192 from both sides those two go away we get 2x equals negative 12 divided by two so we get equals negative six but again the directions say to find the measure of the indicated angle so this angle was bold so if plug in negative 6 for we get negative 6 plus 96 equals that will give us 90 degrees so that is our answer okay let's go to question 26. again very similar to 25 they are consecutive interior angles if we add them up they equal to 180. so 20x plus 24x gives us 44x 5 plus negative 1 gives us positive 4. again that equals 180 let's subtract 4 from both sides cancel out 44x equals 176 now we divide everything by 44 and so we get equals four okay so again we want to solve for the bold so the bold angle was 20 plus five so let's plug in four for that so we get 20 or 24 plus five twenty times four is eighty and eighty plus five equals eighty-five so the measure of that angle is eighty-five degrees okay let's go to twenty-seven just two more problems so 6x and 5x plus 10 are considered corresponding angles we know that they equal each other so if we do 6x equals 5x plus 10 we can solve for we subtract 5 from both sides those two cancel out we get equals 10 very easy now they're asking us to find 6x so let's plug in 10 for 6. 10 for so we have 6 times 10 which gives us 60 degrees so that is our answer the last problem again very similar to 25 and 26 they are consecutive interior angles so they add up to 180. plus equals 2x 109 plus 89 gives us 198 equals 180 subtract 190 from both sides you get 2x equals negative 18 divide by 2 equals negative 9 but that's not what they're asking us to solve so i'm going to box it in blue they're asking us to solve plus 89 so we said was negative 9 so negative 9 plus 89 gives us 80 degrees and that is our answer for question 28.