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>> Julie Harland: Hi.
This is Julie Harland
and I'm Your Math Gal.
Please visit my Website
at yourmathgal.com
where you can search for any
of my videos organized
by topic.
This is Part One of Angles
and Triangles.
And in this video,
we learn what the sum
of the three angles
of a triangle is.
We define an isosceles
triangle, and we do these
three problems.
We're going to talk
about the angles in a triangle
and solve some problems
involving angles
and triangles.
So first of all,
here's just a basical
triangle, and you notice
there's three angles
in a triangle,
and what we need
to know is what the three
measures of those angles add
up to.
Well, one thing you can do is
draw your own triangle.
Just use straight lines,
probably straighter
than I've got right here,
and then write A, B,
and C in the corners.
Do it on a big piece of paper
and then rip off the corner.
So rip off that corner
and then rip off that corner
and then [Inaudible] rip off
that corner so you can see A,
B and C. And start
by just putting this Angle A,
okay, and then right next
to it put Angle B. So here's
like your ripped off piece
of Angle A,
and then you're going
to take Angle B
and put it next to it.
I'm not sure how big it is,
but let's say it something
like this.
So this would be
like your ripped off piece
of Angle B, and then next
to it put your Angle C.
[ Demonstration ]
And if you do this,
you've got these sides all
adjacent to each other.
These angles,
when they're all next
to each other like that,
form a straight line.
See this straight line
right here.
We will form a straight line.
So that's really interesting.
What it's telling you is
if you know the measure
of those, those three angles,
if you add them up,
it adds up to 180 degrees.
So if we call A,
B and C just the measures
of the angles --
I'm going to use little
letters for the measures; A,
B and C, so it could be
in degrees.
It adds up to 180 degrees.
And that's the first important
fact about angles
in a triangle.
If you've got three angles
in a triangle,
their measures add
up to 180 degrees.
So here's a problem.
If two angles
in a triangle have measures 40
degrees and 60 degrees,
what is the measure
of the third angle?
Now I realize some
of you could do this
in your head.
That's fine.
But let's just say how would
we solve this
if we couldn't do it
in our heads.
So how about letting the X be
the measure
of the third angle.
So I'm just going
to write third angle,
but I'm really talking
about the measure of it.
So we know
that if we add the three
angles up, we get 180 degrees.
So you could write 40 degrees
plus 60 degrees plus the
third angle.
We know it adds
up to 180 degrees.
So I've got 100 degrees plus X
equals 180 degrees.
And then if I subtract 100
degrees from both sides,
that tells me X is 80 degrees,
and that is the measure
of the third angle.
Now you don't want
to leave your answer
as X equals 80 degrees
because look
at the original problem.
There was no such thing
as solving the equation,
or it doesn't say what's X. It
says what's the measure
of the third angle?
So you'd write the third angle
is 80 degrees.
Now it could be
that you could leave off this
degree symbol
as you solve the problem,
but then at the end you have
to remember to put it there,
because when you're writing
your equation,
it's just to help you
to find the correct answer.
So some people leave off the
degree symbol
and just write this
so you don't even see
the degrees.
Sometimes they get in the way
of more complicated problems.
So you'd write X equals 80.
And that's why, in the end,
you have to make sure
that you're really writing the
answer to the problem,
which is 80 degrees.
And now we're just going
to check it.
Did those three angles add
up to 180 degrees?
So I've got 40, 60 and 80
and you add it up,
and you make sure it adds
up to 180 degrees.
That's how you know
it's correct.
So here's one for you to try.
So put the video on pause
and try this problem.
Okay. Let's do it.
Let's say that the --
let's call X the third angle.
I'm going to leave off the
degrees this time just
so it doesn't get in the way.
So I've got the 53 plus 68
plus the third angle, is 180.
I really mean degrees.
Right. But to solve this
problem, I'm just leaving it
off temporarily.
So if you add like terms
over here,
I've got 121 plus X plus 180,
and then I'm going
to subtract 121
from both sides, which is 59.
So my answer is what's the
measure of the third angle?
The answer would be 59
degrees, or you could write
that out in words.
The third angle is 59 degrees.
Don't just put 59.
In fact, if you don't want
to put the degree symbol
in there, it's wrong,
because there's another way
of representing angles
without degrees
and it means something
totally different.
So be careful
that you remember to put
that little degree
symbol there.
And let's go ahead
and check it.
We've got 53, 68 and 59.
Let's add them up.
So 3, 8 and 9, that's 20,
right, carry the 2,
and then we've got 7, 11; 180.
It adds up to 180 degrees.
Cool. So 59 degrees was the
correct answer.
All right.
There's a special triangle
called, an isosceles triangle,
and then an isosceles
triangle, two
of the angles have the same
measure, at least two angles.
So let's say this
is isosceles.
Let's say if these two are the
same measure --
I'll call both of those X,
and then the third angle
up here, which I'll call Y,
has a different measure.
In fact, they could all three
have the same measure.
That would also be isosceles.
But usually,
it refers to only two angles
with the same measure.
So here's a problem involving
an isosceles triangle.
In an isosceles triangle,
one angle is 15 degrees less
than one of the equal angles.
Find the measures
of the three angles.
So we don't know any
of the angles here;
so we have
to define all of them.
So let's say we've got one
of the equal angles.
Let's call it X,
and then the other equal angle
would then also be X. Right.
And then what would be the
last angle?
I'll call it the third angle.
This is the one
that is not one
of the equal angles.
It says it's 15 degrees less
than one of the equal angles.
Well, one of the equal angles
is X. So you would have
to subtract 15 from X. Again,
I'm not writing
in the degree symbol.
But in reality,
it would be minus 15 degrees.
Okay. Now we need
to find the measures
of the three angles.
And what do I know
about the three angles
of any triangle?
We know they add
up to 180 degrees.
So we take the first angle
plus the second angle plus the
third angle.
All right.
Can you see the three
different angles?
First angle, second angle,
third angle.
It adds up to 180 degrees.
So we're just going to add
like terms here.
3X minus 15 is 180,
and then I've got to add 15
to both sides; so 3X is 195.
And then we're going
to divide both sides by 3.
[ Demonstration ]
So X is 65.
Now remember that it's not
in degrees yet
but our final answer must be
in degrees.
So let's go back up.
X, what did that stand for?
It stood for the measure
of one of the equal angles.
So one of the equal angles is
65 and so is the other one.
Right. And the third one would
then be 15 degrees less
than that.
So 15 from 65 would be
50 degrees.
So first of all, let's check.
That adds up; 65, 65 and 50.
So we add up.
And yes, it adds
up to 180 degrees.
So the answer then would be
the angles are 65 degrees,
65 degrees and 50 degrees.
Actually, you want to go back
up to the words and see
if that make sense,
if they were 65, 65 and 50.
Let's see, does it make sense?
It says, in an isosceles
triangle, one angle is 15
degrees less than one
of the equal angles.
Is it true that this angle,
50 degrees, is 15 degrees less
than one of these equal ones?
Yes, it is.
You can see
that it's 15 degrees less.
So it does make sense.
And so this is the
correct answer.
The angles are 65 degrees,
65 degrees and 50 degrees.
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Please visit my Website
at yourmathgal.com
where you can view all
of my videos
which are organized by topic.
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