How to Solve a Parallelogram Question on the Math Section of the ACT Question of the Day

hey everyone let's work this act math question the question says that the parallelogram below has consecutive angles with measures degrees and 25 degrees what is the value of so we're looking for and when look at my figure i'm looking for this angle right here and because we're given that this is parallelogram can take the angle and add that to the consecutive angle 25 and that's going to be equal to 180 degrees so i'm going to subtract 25 from both sides and i'm going to get that is equal to 155 degrees and that is answer choice so if you understand this question great you can move on to another one but if you want little bit more information on this type of question i'll go into that now why could say that these two angles angle and 25 add up to 180 degrees well there's little bit of information in this question that we need to be able to do that and first of all said something about it being parallelogram that's what we're given in the question let's talk about what parallelogram is we know that parallelogram is four-sided figure and another name for that is quadrilateral and parallelogram is special quadrilateral that has four sides with opposite sides parallel so we can see that this side is parallel to that side and then we have this side length is parallel to this side length opposite sides being parallel now because we know about this being quadrilateral four-sided figure or four-sided polygon being closed figure we know that the sum of the four interior angles of quadrilateral equal 360 degrees and that's important for you to remember four-sided figure interior angles equals 360 degrees that could come up in several different kind of questions now because the opposite sides of this parallelogram are parallel there's another way we can look at parallelogram as two parallel lines cut by transversal if you've been in geometry you've probably looked at angle relationships related to two parallel lines cut by transversal so here our parallel lines and then we have our transversal right here straight line now we learn lot about the different angle relationships in this and if you'll see this feature right here looks lot like the bottom half of this parallelogram now in some geometry classes you talk lot about the names of the different angles in two parallel lines cut by transversal and that's great and it's good to know because sometimes those type of angle names show up in questions and you've got to know what they're talking about but it's not necessary for this particular question but we'll still try to look at what these angles are called recall that when you have two parallel lines cut by transversal that the two interior angles this angle here and this angle here which in our figure is equivalent to and 25 we know that these are supplementary angles meaning they add up to 180 and that's what we ended up using that's one of the properties that we were able to use to come up with our answer now also note in general we can look at our two parallel lines again these two parallel lines cut by transversal which is very similar to our figure of the upper part of the parallelogram again here now we have two angles but they have the same interior relationship they are supplemental to one another and there's other relationships with the two parallel ions cut by transversal remember you have corresponding so if we know this one that's marked with the double lines it is equivalent to this angle right there and the angle with the one line is equivalent to that one the corresponding angle relationship and there are several others for this particular question what we really wanted to make sure that we knew is this supplemental relationship but based on the interior angles of two parallel lines cut by transversal in general what you want to remember is for parallelogram when we have consecutive angles they add up to 180 which really is the 360 degrees of the total interior angles of the quadrilateral divided by two and that's where we get the 180 degrees and the supplemental relationship that's the relationship we want to remember when we're working with parallelograms again there are other relationships with these angles we can see and explore that would result in the same answer and it's great for you to explore these if you'd like to get some help and go deeper in your understanding but we're going to stop right here for the purposes of act prep if you want to dig farther or look for more examples search for the topics of angles with parallel lines quadrilaterals and parallelograms this is your math question of the day we have lots more videos to help you prepare for the math section of the act subscribe so you'll get our next practice until then practice bit more on your own and when you take the test you'll be glad that you did