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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.
In Part Four of Angles
and Triangles,
we define a right triangle
and solve the two word
problems below;
one involving an isosceles
triangle and the other
involving a right triangle.
This is Part Four
in solving word problems,
dealing with angles
in a triangle.
Remember the sum of the angles
in a triangle add
up to 180 degrees.
And in this problem,
we're talking
about an isosceles triangle.
Remember an isosceles
triangle, there are two angles
that have the same measure.
So let's read through this.
In an isosceles triangle,
one angle is 16 degrees more
than twice the measure of one
of the equal angles, right,
because two
of the angles have the
same measure.
Find the measure
of each angle.
Okay. So put the video
on pause and try this
on your own.
First, define your variables
and write an equation and see
if you can solve it
without any help from me.
Okay. We've got three angles
we're talking about.
So let's just call
that the first, second
and third angle.
You define it
slightly differently.
We know two
of these have the same
measure, right, and we know
that one of them is 16 degrees
more than twice the measure
of one of those equal angles.
So we first need
to define the first
and second angle,
the two equal angles,
using the same variable,
in this case.
So let's use X and X.
And now the third angle is 16
degrees more
than twice the measure
of one of those.
So you've got
to add 16 degrees
to something.
I'm going to leave off putting
the degree symbol,
but in the end of the problem,
we'll have
to remember we are defining
variables and writing an
equation to answer
this problem.
So in the end, you do have
to remember
to write your angles
in degrees.
So 16 more
than twice the measure, well,
twice the measure of one
of these angles is 2X.
So that's how I can define the
third angle.
All right.
So we've defined three angles.
And we know
that when you add the three
angles in a triangle,
it adds up to 180 degrees.
So let's do that.
The first angle plus the
second angle plus the third
angle equals 180 degrees.
So there's the first angle.
There's the second angle.
There's the third.
Some people make a mistake
and just write X plus 2X
plus 16.
Be careful.
All right.
The next step would be
to combine like terms
over here on the left side.
So that is 4X plus 16
equals 180.
And then we solve
that equation.
Now there's more than one way
to solve this equation.
You could subtract 16
from both sides
and divide by 4.
I'm going to do it a little
bit differently like I did
in Angles and Triangles,
Part Three.
If you have a common factor
in all your terms,
you could divide
by that common factor
to make the number smaller.
So I noticed that 4 goes
into all three
of those numbers.
So if I divide both sides
by 4, I just get easier
numbers to deal with.
This is an optional way
of solving this equation.
So that gives me X plus 4
equals, and then 4 goes
into 180 --
well, 2 goes into it 90
and 2 goes into 90, 45's.
That's 45.
And then I just subtract 4
from both sides.
[ Demonstration ]
Now you didn't have to use
that method.
You could have certainly
subtracted 16.
Right. So over here,
I'm going to write
down the other way
that somebody else might have
done it.
It's the more traditional way.
I don't like to always
be traditional.
I like the idea
that I have options.
So I could subtract 16
from both sides.
I get 4X equals 164.
And then when you divide by 4,
you still get X equals 41.
The point is one
of the equal angles is
41 degrees.
So that's what matters.
41 degrees and 41 degrees,
that should be the two
equal angles.
And then what would the third
angle be?
It says it's 16 more
than twice the measure.
All right.
So if we take 41
and we double it, we get 82.
And it says it's 16 more
than that.
So otherwise,
I'm not even putting
in 2X plus 16.
I'm using my common sense.
If somebody tells me it's 16
more than twice it and I know
that one of them is 41,
I'm just saying, well,
2 times 41 is 82 and 16 more
than that.
So this would be 98.
So now the question is does
that make sense?
First of all,
is it true
that this third angle is 16
more than twice one
of the equal angles?
And that's certainly true.
We did it over here.
What's the other thing
to check?
That the angles add
up to 180 degrees.
So let's check that out.
[ Demonstration ]
41, 41 and 98, and add up.
We get 180.
It does check out.
So the answer
to this problem is find the
measures of each angle.
You could just say, well,
it's 41 degrees.
These are the measures
of the three angles.
You could write this
in words too,
which I like to
write sometimes.
The angles add up to --
I mean, I would say the angles
are 41 degrees, 41 degrees
and 98 degrees.
And there we've got
our answer.
All right.
I want to talk
about one kind --
another kind
of special triangle.
We talked about the
isosceles triangle.
Now we're going to talk
about the right triangle.
In a right triangle,
one of the angles is a right
angle; so its measure is
90 degrees.
So a right triangle looks
something like this.
One of the angles is a right
angle and 90 degrees.
In some countries,
they call this a
right-angle triangle.
All right.
Things are different,
depending on where you happen
to live.
All right.
So let's just do a problem
having to do
with a right triangle.
And what does that tell you
about these other two angles?
If this one's 90 degrees,
what do these other two have
to add up to?
Well, altogether they're 180.
So these other have --
other two have to add
up to 90 degrees.
So they're complementary.
So by the way,
the other two angles --
[ Demonstration ]
-- are complementary, --
[ Demonstration ]
-- since they add
up to 90 degrees.
[ Demonstration ]
[Inaudible] fit in there.
Let's move this
over so you can read it.
Okay. So they would be
complementary angles.
So now let's just do a problem
having to deal
with a right angle.
So here's our problem.
In a right triangle,
one of the angles measures
38 degrees.
Find the measures
of the other two angles.
This isn't so bad.
We've got three angles.
Right. So we've got the first
angle, the second angle
and the third angle.
One of them is 38 degrees.
They told us.
All right.
What else do we know
about a right triangle?
What is one of the measures
of the other degrees?
90 degrees,
that's the right angle.
So all I need is my third
angle X. Now there's two ways
you might figure this out.
You could add all three;
X plus 90 plus 38 equals 180.
I'm putting
in the degrees later.
Someone might write all three
angles to add up to 180,
and someone else might realize
that the two smaller angles
just add up to 90.
So someone else just might
write X plus 38 equals 90,
correct, because they're
complementary,
the two other angles.
So it doesn't matter which one
of these equations you write.
You should be able to find
out what that third angle is.
And then, of course,
it says find the measure
of the other two.
Well, one of them is 90.
That's a given,
since it's a right triangle.
So what does this give us?
X plus 128 equals 180.
I just subtract 128
from both sides.
[ Demonstration ]
And that would give us X
equals 52.
That would end
up being 52 degrees.
Right. And this one we just
subtract 38.
A different person may have
solved it this way,
and they also got 52 degrees.
So it doesn't matter
which way you think about it.
You know that one
of the angles is 90,
and now you know the other one
is 52.
So that's all you would
write here.
The other angles are 52
and 90 degrees.
And actually,
instead of saying are,
I like to write the other
angles measure --
measures are.
Okay. That's just a
little formality.
Okay. So that's our answer.
And we could do a little check
to make sure that, of course,
38 plus 52 plus 90 equals 180.
That's pretty simple
to verify.
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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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