Triangle angle example 1 | Angles and intersecting lines | Geometry | Khan Academy

Figuring out angles in a triangle. A little about exterior angles being the sum of the remote interior angles

Missed the previous lesson?

Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Geometry channel:

[TurboSol]

I haven't done one of these in a couple years so I paused it and tried, I did it by adding up 31+64+50 = 145, then subtracted 145 from 180 = 35. I totally forgot the method of supplementary angles, that is helpful.

[brantmorenodiaz]

Your videos has helped me a lot. My math teacher uses your vids to help us in math problems, so I thank a lot to my teacher for showing these videos. Hope you doing well and keep on making math videos. :)

[jojochima]

This was really helpful. I'm about to do a test on it and I think I'm ready

[sekharrgaddam]

You have a nice heart and your good at math like how salmon khan is good at acting May God bless you

[RobynHuff]

Yeah this is a round-about way to solve the problem, and Sal probably knew that. His purpose is to get people to understand math, not just to solve the problem, and doing this in multiple steps lets him explain more than if he had done it in one step.

[mackingu]

A more intuitive solution for Z is made evident (at least for me) when you realize that the two triangles shown form a larger triangle.

For z:
180 - 64 - 31 = 85
85-50 = 35*

Alternative solution for y:
180 - z - 31 = y (since you know z from above)

[neerajbalani]

Or you could simply do: 180 - 64 - 31 - 50 = 35! Would be much quicker, because you know all angles in a triangle add up to 180.

[sanrafaa]

As soon as I saw the problem, I managed to solve it just by my mind, inside 10 seconds... !! Sal explained it for too long and also the method is twisted ! But i won't give a dislike to this video or any of Khanacademy videos !

[kingchawdhry]

I didn't understand angle sums before but when i saw ur video it helped me and i got 100% in my test. Many thanks!

[onesandzeroes]

As others have pointed out this is a VERY roundabout way of solving this problem. Just take the big triangle, add the given angles, and subtract them from 180

[madhavchapadi]

Similarity chapter problem involving area of model or map with full details converting to km to cm or km square to km

[SEThatered]

@UMULAStudios
I just happened to have a stopwatch on my table so i timed it.
And this problem is super easy:
if you ignore the dividing line you'll see a big triangle with 64° and 31° known angles.
The remaining angle is 180° - (64°+31°) = 85° and this corner is divided into 50° and (85 - 50) = 35° here you go.
No need for complex calculus here at all.

[atasha]

what I did at the start when i didnt knew the solution was:
180-(50+64+31) = z
I got 35

[tutstorial]

u could let x be the angle u want to know,


so that (50 + x) + 64 + 31 = 180

[BitchesBeerBacon]

I invented this method in 1996 in West Palm Beach Florida. Wellington landings middle school.

[mia]

My teacher posts every lesson on her youtube channel but I didnt understand it so i came here.

[oliverwood]

what program are you using to do that?

[erratic]

I see where you told us about two triangles, but not where you told us about the greater triangle. It looks like the assumption is made that the bottom of the greater triangle is actually a straight angle. IOW I see a tall skinny nearly isosceles triangle and a short squat nearly isosceles triangle glued together at equal length segments with some angle measures given and some excluded. I'm thinking the supplementary angle assumption is premature. Am I wrong about this?

[mrowner]

Haha like everyone else is saying, this could have been done in under a minute :P, very well explained though!

[redpillreality]

@UMULAStudios i did it in under 30 sec in my head. once u know how to solve it there are ways of doing it. im also good at mental math doing it in my head