Triangle Angle Example 1

Geometry

Angles with triangles and polygons

Proof - Sum of Measures of Angles in a Triangle are 180
Triangle Angle Example 1
Triangle Angle Example 2
Triangle Angle Example 3
Challenging Triangle Angle Problem
Proof - Corresponding Angle Equivalence Implies Parallel Lines
Finding more angles
Angles 1
Angles 2
Sum of Interior Angles of a Polygon
Angles of a polygon
Sum of the exterior angles of convex polygon

Triangle Angle Example 1 Figuring out angles in a triangle. A little about exterior angles being the sum of the remote interior angles

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Triangle Angle Example 1

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what i want to do now is just a series of problems
that really makes sure that we know what
we are doing with parallel lines and triangles
and all the rest. And what we have right here is
a fairly classic problem. And what I want to do is
I want to figure out just given the information here
so obviously I have a triangle here I have another
triangle over here we were given some of the angles inside of these triangles. Given the information
over here I want to figure out what the measure of this angle is
right over there I want to figure out what that question mark is. And so you might want to give a go
at it just knowing what you know about the sums of the measures of the angles inside of a triangle and
maybe a bit of what you know about supplementary angles so you might want to pause it and give it a try
yourself since I'm about to give you the solution. So the first thing you might say and this is a general
way to think about these problems where they give you some angles and you have to figure out other angles
based on sum of angles in a triangle equaling 180, or this one doesn't have parallel lines but you might
see one with parallel lines and supplementary lines and complementary lines is to just fill in every
thing that you can figure out and one way or antoher you can probably figure out what this question mark
is. So the first thing that pops out to me is that we have one triangle right over here, we have this
triangle on the left, and on this triangle on the left we are given two of the angles. And if you have
two of the angles in a triangle you can always figure out the third angle because they are always going t
o add up to 180 degrees. So if you call that 'X' we know that 'X' plus 50 + 64 is going to be equal
to 180 degrees. Or we could say X plus 114 is equal to 180 degrees, we can subtract 114 from both sides
of this equation and we get 'x' is equal to 180 minus 114 so 80 minus 14, 80 minus 10 is 70 minus another
4 is 66. So x is 66 degrees now if x is 66 degrees you might find that there is another angle that is
not too hard to figure out. So let me write it like this, so x, is equal to 66 degrees. Well if we
know this angle right over here, if we know the measure of this angle is 66 degrees. We know that that
angle is supplementary with this angle over here, there outer sides form a straight angle and they are
adjacent. So if we call this angle right over here y we know that y plus x is going to be equal to 180
degrees and we know x is equal to 66 degrees, so this is 66 so we can subtract 66 from both sides and
we get y is equal to 180-66 is 114 and that number n=might look a little familiar to you. notice this
114 is the exact same sum as these two angles over here. And thats actually a general idea and ill do i
t on the side here just to prove it too you. if i have lets say these two angles lets say the measure
of that angle is a, of that angle is b, the angle of this measure we know is going to be 180 minus a
minus b, thats this angle right over here. And then this angle which is considered to be an exterier
angle, so in this example y is an exterior angle in this example that is our exterior angle that is going
to be supplementary to 180 minus a mius b so this angle plus 180-a-b is going to be equal to 180 so if
you call this angle y you are going to have y plus 180 -a -b is equal to 180 you can subtract 180 from
both side you can add a and b to both sides so +a +b +a +b I'm running out of space on the right hand
side. and then you are left with - these cancel out - on the left hand side you are left with y on t
he right hand side is equal to a plus b. so this is just a general property. you can you can just reason
it through yourself just with the sum of the measures of a inside of of an the angles of an inside of
a triangle add up to 180 degrees and then you have the supplementary angles right over here or you van
just say look if I have the exterior angles right over here it is equal to the sum of the remote interior
angles thats just a little terminology you'd see there so y is equal to a +b , 114 degree we've already
shown to ourselves is equal to 64 + 50 degrees, anyways regardless of how we did it if we just reason i
t out step by step or if we just knew this property from the get go if we know that y = 114 degrees and
I like to reason it out every time just to make sure I'm not jumping to conclusions. So if y is 114
degrees. we know this angle we know, we were given this angle at the beginning know we just have to
figure out this third angle in this triangle. so if we call this z, if we call this question mark is
equal to z we know that z + 114 +31 is equal to 180 degrees. the sums of the measures of the angle i
side of a triangle add up to 180 degrees, that is the only property that we are using at this step.
So we get z plus what is this 145 145 = 180, did I do that right if I we have a 15 and a 30 yep 145 is
equal to 180. subtract 145 from both sides of this equation and we are left with z = 80 - 45 is equal

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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

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When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...

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At 2:33, Sal says "double bonds" but should say "single bonds."

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