TjenigC#iieet Jtus L0m t hite "nurntWivei=LuryEBFor problems 35 through 38,find the measure of each angle in parallelogram WXYZ (the figure is shown on the rig...

In the diagram, $\overrightarrow{O T}$ bisects $\angle S O U, m \angle U O V=35,$ and $m \angle Y O W=120 .$ Find the measure of each angle.
$$m \angle Z O Y$$

Problem here provides us with this diagram in the measurement of these angles and asks us to find the measurement of angles e o w. So first, let's find Rosie O ws that z o w So we're looking for We'll do it in a different color here. Well, we're looking for this angle here, and we know that this single and from this single here is 120. So once I find the measurement of the single here, I could just add it to the 1 20 And I'll know the measurement of Ankle zow. And so we know from vertical angles that this angle here and the angle that's over here see if we can pick a different color here. So this angle and this angle are equal to each other because they're both verdict because their vertical angles and so the angle. And here is 35 degrees. And so all I have to do is add this 1 20 to the 35 to get the total measurement of angles e oh w. And so that's 35 plus 1 20 which is 1 55 So that's they enter to best one here

And this problem. We're looking for the measure of a missing angle. How bingle we're missing is the measure of angle M. P. And so I m he and is here that angle there. We know a few things about this shape were given, um, first that l m and P is a rectangle and p. So that's a rectangle as well as the fact that, um okay, MJ is a parallelogram. We know that the measure of angle M. J and is 35 degrees. So m j n is here 35 degrees. Um okay, So because this is a rectangle Elham and and P, we know is also parallelogram and opposite sides of parallelogram are concurrent, so I won't label thes twerking grams and these two my congrats. We also know that in a, um, rectangle, the diagonals are of equal length and in a parallelogram, they buy sick each other. And so therefore all three of thes are of equal length. Great are all four of those because they're equal when they bite each other. Now we have a triangle and I saw cities triangle here that we can pull out. Um well, first, before we do that. Let's look at this straight angle we have. We have a 35 degree angle and we have something. Those have to add up to 180. So 180 minus 35 will give us needing money. 35 gives us 145 degrees. So this is 145 degrees. So this is 145 degrees. Um, we destroyed that on the 45 degrees. Okay. And so we're almost there, cause we also we have a nice softly strangle. Um, so this I saw sleaze. Triangle is triangle P. J. And we have those sites are congruent, and we have 145 degree angle here. Um, and we know that these two angles must become groups is nice. Also is triangle eso We know that 145 last two times recalled his ex equals 180. If I subtract 145 from both sides, I get two x equals 35. Um, therefore, if we divide by to read too, um, X equals 17 17.5 degrees. And that was the angle. We're looking for the single here, so that measuring goes 17.5 degrees

In this kite. We want to find the measure of angle vz wide. So I'm just gonna look at this triangle right here. The Z. Why? I want to figure out what this angle is. So it tells you that this angle is 49 and then in a kite, the diagnosed meet at right angles. So this is 90. So if I do 90 minus 49 that will leave me with 41. And so angle vz y equals 41 degrees.

Okay, so we know that the measure of angle one is going to be 30 degrees, and I'm looking for a different angle measure, so I'm looking for the measure of angle seven down here. Okay, so but I do know is that in a rectangle I have parallel lots. So, um, indirect angle opposite sides or parallel. And given a trans verceles, I could find different angles. So if I know the measure of ankle one, for instance, and I have a trans Mursal that cuts through two parallel lines that I know that alternate interior angles are equal. So this angle down here will be the same as ankle one, which will be 30 degrees. I also know that in a rectangle, each corner is 90 degrees because the definition of a rectangle is a cuadrado with four right angles. So, um, it defined this angle measure. I know that it's going to be 90 degrees minus 30 degrees, which will end up being 60 degrees. Okay, but I still haven't found the measure of angle seven. Let's apply a couple more properties to erect tangle. Well, I know that the diagonals are equal and they bisect each other. So if they're equal and they bisect each other, these two sides will be equal. And this is an example of an eye sauce Elise trying, um or it at least has two sides equal, so the angles opposite of those sides will be equal. So measure of angle seven will be the same as the angle over here, which will be 60 degrees.