# Triangle angle example 2 | Angles and intersecting lines | Geometry | Khan Academy

We’re given a

bunch of lines here that intersect in all different

ways and form triangles. And what I want to

do in this video, we’ve been given the measures of

some of the angles, this angle, that angle, and that angle. And what we want

to do in this video is figure out what the

measure of this angle is. And we’re going to

call that measure x. And so I encourage you to pause

the video right now and try it yourself. And then I’m going to

give you the solution. So I’m assuming

you’ve unpaused it. And you’ve solved it

or you’ve given it at least a good shot of it. So let’s try to do it. And what’s fun about

these is there’s multiple ways to solve these. And you kind of

just have to keep figuring out what

you can figure out. So let’s say you start on the

left-hand side right over here. If this is 121 degrees,

then you’d say, well look, this angle right over here is

supplementary to this angle right over there. So this is 121 degrees

plus this green angle, that has to be equal to 180 degrees. So this is going to

be 180 minus 121. Let’s see, that’s the

same thing as 80 minus 21. 80 minus 20 would be 60. So that’s going

to be 59 degrees. So let me write that down. That’s going to be 59 degrees. Now we see that we have

two angles of a triangle. If you have two

angles of a triangle, you can figure out

the third angle, because they need

to add up to 180. Or you could say that this

angle right over here– so we’ll call that

question mark– we know that 59 plus

29 plus question mark needs to be equal

to 180 degrees. And if we subtract the 15 out

of the 29 from both sides, we get question mark is equal to

180 minus 59 minus 29 degrees. So that is going to be 180

minus 59 minus 29, let’s see, 180 minus 59, we

already know, is 121. And then 121 minus 29. So if you subtract

just 20, you get 101. You subtract another

9, you get 92. So that’s going to be

equal to 92 degrees. This is equal to 92 degrees. Well, this right here

is equal to 92 degrees. This angle right here is

vertical with that angle. So it is also going to

be equal to 92 degrees. And now we’re

getting pretty close. We can zoom in on this

triangle down here. And let me save some space here. So let me just say

that that over there is also going to be 92 degrees. And at this triangle

down here, we have two of the sides

of the triangle. We just have to

figure out the third. And actually, we don’t even

have to do much math here, because we have two of the

angles of this triangle. We have to figure

out the third angle. So over here, we have one angle

that’s 92, one angle that’s 29. The other one will be

180 minus 92 minus 29. And we don’t even have

to do any math here, because essentially, this is the

exact same angles that we have in this triangle

right over here. We have a 92 degree angle,

we have a 29 degree angle, and the other one is 59 degrees. So in this case,

it has to be also 59 degrees, because over

here they added up to 180. So over here, they’ll

also add up to 180. So that will also

get us to 59 degrees. We could just get that by

taking 180, subtracting 29, subtracting 92. And then if this is 59

degrees, then this angle is also going to be 59

degrees, because they are vertical angles. So we’re done. x is

equal to 59 degrees. Now there’s multiple

ways that you could have reasoned

through this problem. You could have immediately

said– so let me start over, actually. Maybe a faster way,

but you wouldn’t have been able to do kind

of this basic steps there, is you said, look, this is an

exterior angle right over here. It is equal to the sum of

the remote interior angles. So 121 is going to be 29 plus

this thing right over here. And we ended up doing that when

I did it step-by-step before. But here, we’re just

using kind of a few things that we know about

triangles ahead of time to maybe skip a step or two. Although I like to do it the

other way just so we make sure we don’t do anything weird. So anyway, this

is going to be 129 minus 29, which

is going to be 92. And if this is 92, then

this is also going to be 92. And then, if this is x, then

this is also going to be x. And you could say x plus 92

plus 29 is equal to 180 degrees. And then you’d say

x plus 92 plus 29 is going to be 121 degrees. We already knew that before. And so that is going

to equal 180 degrees. And so x is equal to 59 degrees. So there’s a ton

of ways that you could have thought

about this problem.

simplest is to see that the lines are parallel,due to the 29 degree angles,so 180 minus the exterior angle 121 gives the angle which is the same as x

KHAAAAAAAAAAAAAAAAAN!!!!

Took 13 second. 180-121=59

fucking easy homeboy

nice

he was wrong about the 92 degrees perpendicular lines intersect at a 90 degree angle so i solved it in under 30 seconds because 180-90-29=61

Or you can do 121 x 2 = 242 , 360-242= 59 and since it is parallel that means X is 59

Don't tell me you learned this in primary school!😏

I've learned more here than in my 8 months in math class

Khan academy is very help ful

Most helpful

Makes hard problems look easy

Figured it out in 4 seconds. (I'm in 7th grade)

We have two lines, each with a 29-degree angle. That makes them parallel lines (I'm not explaining why). On the left side of the plane, one of the angles is 121 degrees, and since the two lines are parallel, that carries over to the other line, making 121+x=180 (supplementary angles). Simple math figures out the rest. None of that complicated stuff is required in this case, but its usually a good idea to know this, if the two lines' angles are not equal.

Thank you very much, God bless you. I am a science student learning maths for gre and its helping me greatly. Thank you very much.