# Find measure of vertical angles | Geometry | 7th grade | Khan Academy

So we have two

intersecting lines here, and then we have this

other purple-looking line. And then they’ve

given us some angles. They tell us that the measure

of this angle right over here is 7x. The measure of this angle

right over here is 60 degrees. And the measure of this

angle right over here is x. So let’s try to figure out

what all of these angles are. So to do that, we have

to figure out what x is. And there’s a big clue here,

because the 60-degree angle plus the x angle,

they’re adjacent. And if you add these two angles

together, their outer rays, our vertical angle

with this 7x angle. So we could say– and just to

visualize that a little better, let me color it in. Actually, let me do it this way. You see that this

angle out here– let me do it in a color

I haven’t used yet. This entire angle

over here, which is going to be 60

degrees plus x, that’s a vertical angle with

this angle, the one that has measure 7x. So we could say that 60

degrees plus x is equal to 7x because vertical

angles are equal. So let’s write that down. We get 60. And we’ll assume that

everything is in degrees. 60 plus– let me do that

in this other color. 60 plus x is going

to be equal to 7x. And now we just

have to solve for x. So the simplest

thing to do would be to get all over x’s on

one side of the equation. I’ve already gotten seven

x’s on this right-hand side, so let’s get rid of all of

the x’s on the left-hand side. And the easiest way

to get rid of this x is to subtract x from

the left-hand side. But of course, in order

to keep it an equation, we can’t just do

something to one side. Otherwise, it won’t

be equal anymore. We have to do it to both sides. So let’s subtract

x from both sides. And on the left-hand side,

we are left with just the 60. So we’re left with just a 60. And then that is going to

be equal to 7x minus x. If I have 7 of something

and I get rid of 1 of them, I’m going to have 6 of

that something left. So that’s going

to be equal to 6x. So we have 6 times

something is equal to 60. You could probably figure

that out in your head. But I will do it a

little systematically. We can divide both sides

by 6 to solve for x. So let’s do that. And we would be left

with x is equal to. 60 divided by 6 is 10. And we reminded ourselves that

everything was in degrees. And we could even do that here. This was in degrees. This is in degrees. And so this is in

degrees right over here. So the measure of this angle

right over here is 10 degrees. So this one right over

there is 10 degrees. This is, of course, 60 degrees. You add them together, 60

degrees plus 10 degrees is 70 degrees. So this bigger angle right

over here is 70 degrees. And of course, this one over

here, it’s a vertical angle. It’s going to have

to be the same. And we see that, 7 times x. 7 times 10 degrees is

70 degrees as well.

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