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# Worked example: Triangle angles (diagram)

We have a right triangle that's split into several smaller right triangles. The angle measures in any triangle always add up to 180 degrees. By using this fact and looking at complementary (adding up to 90 degrees) and supplementary (adding up to 180 degrees) angles, we can find the missing angle measures in the triangles. Created by Sal Khan.

## Want to join the conversation?

• what does the little O with the - beta thing mean??
• theta is the greek letter representing the unknown. In math, it represents an unknown angle whereas a letter represents a variable.
In trigonometry, theta is used frequently
• Everyone is asking about theta, but what if there are two angles you need to figure out? Do you label one theta and the other theta2, or is there a different symbol used?
• You're right. You can use theta1 and theta2 (the 1 and 2 will be a subscript, sometimes spoken "theta sub 1").

Other perfectly valid ways of representing other angles is to use other Greek letters. Alpha (α) and beta (β) are very often used to represent unknown angles.

Even the favourite 'x' gets used frequently for angle. It depends on the author and providing there's no ambiguity, whatever letter you choose is fine.
• Sal's algebra in his first approach for solving the problem reminded me of a question: when doing that sort of algebra, do you treat the numbers individually with the positive/negative sign before it? For example: 90-5=x. Could you treat the 90 as +90 and the 5 as -5?
• To answer your question: Yes you could treat the 90 as +90 and the 5 as -5. Try it. -5+90 and you still get the same answer as you would get with 90-5.

Try another: -80 + 10 which would equal -70. If you flipped the problem but kept the signs it would be (+)10 - 80 which would also give you -70

hope this helped!!
• Is "beta" the same as "theta?"
• Beta and Theta are 2 different Greek letters, but they can both be used as variables, like x & y for angles. If you are asking whether it matter which one you use as a variable, it doesn't matter, they both work. But, if you are asking whether they are the same letter, they are not the same.
• Since when did they use Greek letters? Is the English alphabet not enough for math that is supposedly for numbers?
• I have a grapefruit rn
who wants it?
• the comment section did not dissapoint XD
• where did the o come form
• That's not an "o". That's the greek symbol θ, or theta. I don't know why Sal chose this specific letter for this example, but Sal does as Sal wants.
• Ima cry why is this kinda hard
• do I learn angles in 5th grade
• interesting... But will actually have problems were the triangle is split into different parts or it is always like that?
• what is the formula to find the degrees in a triangle that 180degrees largest is 25 degrees more than the smallest the some of the 2 smallest is 30 degrees more than the largest
• One way to do it is to make a system of equation:
let a be the largest angle and b, c be the smaller two angles, and a + b + c = 180
a - 25 = c
b + c = a + 30
Notice that b + c = 180 - a
You can now rewrite the second equation by substituting b + c with 180 - a so that you only have to deal with 1 unknown term:
180 - a = a + 30
Rearrange the terms you get:
2a = 150
a = 75
Now using the previous equations you can figure out the rest of the terms:
c = a - 25 = 75 - 25 = 50
b = a + 30 - c = 75 + 30 - 50 = 55
and there you go :D
a = 75, b = 55, c = 50
So I guess there is no "formula" to do these questions, but as a matter of fact, there are many ways to approach problems like this. It's all about figuring out a way, like solving a puzzle.
I hope this helped