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A triangle has sides of length 20,21,and 36_ Find the measure of all three of the angles, to the nearest tenth of a 'degree,and draw picture of this triangl ro...

Question

A triangle has sides of length 20,21,and 36_ Find the measure of all three of the angles, to the nearest tenth of a 'degree,and draw picture of this triangl roughly to scale. (Hint: Find the measure of the largest angle first!)

A triangle has sides of length 20,21,and 36_ Find the measure of all three of the angles, to the nearest tenth of a 'degree,and draw picture of this triangl roughly to scale. (Hint: Find the measure of the largest angle first!)



Answers

The measure of the smallest angle of a triangle is one-third the measure of the largest angle. The middle angle measures $30^{\circ}$ less than the largest angle. Find the measures of the angles of the triangle. (Hint: Recall that the sum of the measures of the angles of a triangle is $180^{\circ}$.)

These kinds of problems are sometimes hard to self because there as much of a reading problem as they are of a math problem. So you need to read through the problem. An angle of a triangle is five times greater, then another. The measure of the last angle is three times the measure of the smallest. What are the measures of all three angles? Right, so that sounds like a bunch of gibberish. So you need to break it up into the smaller pieces. So the first thing I always do is what is my goal? What am I looking for? I'm looking for the measures of all the angles. So I've got a triangle. I know that because it says right here told me I'm looking at a triangle, so I'm gonna draw a triangle, and I have no idea, because it was all gibberish to me what my triangle looks like. So I'm just gonna draw a generic triangle. Now I need to pick out the pieces So this verse isn't the first line. Says an angle of a triangle is five times greater than another. Okay, so the angle is five times greater than another. So it doesn't tell me what that other ones, but usually when we have another, that's our axe and then I've got another one that's five times that. So it's gonna be five acts. Then I need to figure out the measure for this angle. So if I keep reading and it says the measure of the last angle my last angle if I look, here's my last single is three times the measure of the smallest. Well, if this is five X Mrs X, this is the smallest. So this is three times the measure of the smallest, so that one has to be three x. Now that I have my angles identified by ax. Now I can go through and say my first angle, plus my second angle, plus my third angle, it's gonna equal 180 degrees. And so I've got one plus 56789 I've got nine X equals 180 degrees. And if I divide both sides by nine to get X by itself, X equals 20 so it's 20 degrees, so this angle is gonna be 20 degrees and my five times 20 is gonna be 100 degrees and three times 20 is gonna be 60 degrees, and you can just spot check that cause 20 plus sixties 80 and 80 plus 100 is 180. So, yes, it does equal up to be 180 degrees. And then you just have to look at How did they How did they want you to show your answer? A lot of times, I just want you to write 20 degrees and 60 degrees and 100 degrees.

When working with triangles. The most important thing you need to remember is that it doesn't matter how big or how small this triangle is. The measure of the single plus the single plus the single all three interior angles of the triangle will always equal 180 degrees. So when you're given a triangle and they want you to figure out the measures of each angle of the triangle, they've given you everything that you need to solve this problem right here. So what they're saying, what you need to understand is that this single plus the single plus a single when we add them together, they're gonna equal 180. So we have four x los axe plus X plus 108 because this whole angle is X plus 108. So you gotta have that. So I have the first angle, the second angle, and then there's the third angle. So all those angles together, when we add them up, that's gonna equal 180 degrees. So go ahead and combined. You're like terms. So I have four x plus X plus X is gonna give me six X plus 108 equals 180. And I'm trying. I mean, isolate myself. That's 108. Sorry, I'm gonna isolate my six x some to subtract 108 from both sides for six X equals, um 72 and then to get X by itself into divide both sides by six. So X equals 12. And that's again, not the instrument question, because the question said, What is the measure of each angle? Well, if X equals 12 then yes, this angle is 12 degrees, and this ankle is angles four times 12 which makes this angle 48 degrees. And this angle is 12 plus 108. So 12 plus 108 makes this angle 120 degrees. So the measures of the angles are 48 degrees, 12 degrees and 120 degrees.

Problem. 64. In this problem, let us assume the it's more or less angle. B X. Then, according to the question, the largest angle off the triangle is 90 degrees less next, and that hard angle that is the remaining angle off the triangle is equal to cardi, degree less X. Now we know that for any triangle, it's more less tangle. Less largest angle plus remaining angle is equal to 1 80 degree, so we can write X plus 90 degree blast. Sex plus 30 degree plus X is equal to 1 80 degree. This will give us executed too 20 degrees. This is W. The smallest angle of the dangle and large. Just angle will be 90 degree plus 20 degree that is 110 degrees, and that hard remaining angle of the dangle will be remaining angle. We'll be tardy degree more than their smallest angle, just 50 big. These does that. Three angles off the triangle are competing for 110 degree and 50 degrees

The number eight. So we're not bad. Two angle, but so this is the smallest and Olympic triangle, and therefore, this is the largest angle. So, you know, there are some of the angles of the triangle. Article one into dignity. She can dye air, plus m plus s equals 200. This is the question. Then it is going that that small longer is to industry smaller than the amount. So as the Jakarta am minus 12, Oregon, right in an M minus s or total. That is the question and the queen and then saying that large angle it, some of them we didn't want the smaller a logical to process. Okay, so that is a Puerto good and treat or three questions where to find it and got drunk. Let's do it. None of the dedication one and plus M Plus s a physical quantity. I can see my question three is implementing. So you can take. And in prison places get back to another is about one introduction. Same place to a logical 200 degrees. So a logical to quality buy two for tonight. So we got one more able eligible tonight. All right, so illogical them process. So now my question three. You can try it out. M plus, this is equal to 19. My question to you is there. That is AM minus s. Contractual. My book artist. Two questions. Okay, so you can see assess cancer. So to the musical, to 100 to whatever was said by two. A magical 202 by two. There's a photo Do you want? So, God, I am allergic contact. Do you want not available? Okay, so now I can use the best music creation three. Again. The question three. So a logical, um process. So S e Jakarta and minuses. Okay, so what is? Yes, 19. My next trip to Cuba. Physical too. Continue. He got a cynical to 29. So you've got all three angles. This I can write small longer. The Jakarta verses. 29 degrees and medium. And get as you come to, um, to one degree. And you are younger. It's a call to Jakarta. 90 degree. This is the financing. Okay. Thank you.


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