WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over angles of a triangle.
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Remember a triangle is a polygon with three sides; three straight sides.
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Which means that there are three angles; those sides form three angles.
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All triangles have three angles.
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Here is one; here is another one; there is a third.
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To name this angle here, we can say angle BAC.
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That would be this angle right here; angle BAC.
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But since the A is a vertex and there is only one angle
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that this is a vertex for, we can just call this angle, angle A.
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This one, I can just call angle B; this is angle C.
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Again only if the point A is a vertex for just a single angle.
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Let me give you an example of what it is not.
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If I have an angle like that, I have two adjacent angles; this is A.
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I can't call this angle, angle A, because there is three different angles formed here.
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There is this small angle; there is this angle; there is this big angle.
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This point, this vertex, is a vertex for three different angles.
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In this case, you cannot call it angle A; you can't say angle A.
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You would have to name the other three points like this one.
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You would have to name, if this is B and this is C, then you have to say angle BAC or like that.
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But again this one, because in a triangle, there is only three angles and three vertex.
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You can just name this as angle A.
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If I say angle A, I am talking about this angle here; angle B; angle C.
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Within the three angles of a triangle, remember each angle has an angle measure, the number of degrees.
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All three angle measures is going to add up to 180,
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like the supplementary angles where we have two angles that form a straight line.
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That adds up to 180.
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Here the three angles of a triangle also add up to 180.
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If this is 60, this is 60, then what I can do is add these two up and subtract it from 180.
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Here if I want to write an equation, I can say measure of angle A.
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Remember this M is for measure; it is to show the number of degrees.
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Measure of angle A plus the measure, the number of degrees, of angle B
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plus the measure of angle C is going to equal 180 degrees.
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We know what the measure of angle A is; how many degrees is angle A?
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We know it is 60; this whole thing is just 60 degrees.
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Measure of angle A is just 60; I can just replace this with 60.
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Do I know measure of angle B?--no; I can just leave that there.
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Plus the measure of angle C is also 60.
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That is all going to add up to 180.
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Again I can just add these two together which is this and this.
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That is going to be 120; plus this unknown adds to 180.
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I can subtract this from 180; 180 minus these two; whatever is left over.
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From the 180 total, if I add these two together
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and then figure out how many degrees are left over from the 180,
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then all of that, all of those left over degrees have to go to angle B.
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I am going to subtract; measure of angle B is going to be 60 degrees.
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The leftover degrees from the 180 is 60; then this also has to be 60.
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That is how you are going to solve for the missing angle measure.
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Remember if we are going to be solving for the missing angle measure,
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then we have to know two of the three angle measures.
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I can't only have the measure of angle A and then find both B and C
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because they are going to be different angles; they could be different angle measures.
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I don't know how many are going to go here and how many are going to go here.
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To find the missing angle measure, you have to have two out of the three like this one.
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I have measure of angle A, 70 degrees.
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I have the measure of angle B; that is 60 degrees.
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I want to find the measure of angle C, meaning I want to find how many degrees is in angle C.
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Again I can just take these two, add them together; how many from the 180?
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I know that this plus this plus this all have to add up to 180.
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This and this are used up.
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However many are left over all have to go to angle C.
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I can say 70 degrees plus this 60 plus the measure of angle C.
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This is the proper way to write it.
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I can't just write C because you are talking about the measure, meaning how many degrees.
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It is all going to add up to 180.
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Again I am going to add these two together.
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This will be 130 plus the measure of angle C.
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130 being used up plus the leftovers is going to equal 180.
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Remember I subtract 180 with this number.
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That way measure of angle C is going to be 50 degrees.
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That means this has to be 50.
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60 plus 70 plus 50 is going to add up to 180.
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That is the missing angle measure.
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Determine the angle measures if the angle measures could be the angle measures of a triangle.
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Three angle measures for the three angles of a triangle.
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If they add up to 180, then they can be the correct angle measures of a triangle.
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But if not, if they don't add up to 180,
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that means they can't be the three angle measures of a triangle.
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The first one, I am going to take 50 plus the 90 plus the 40.
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Just add them all up; I know that 0 plus 0 plus 0 is 0.
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5 plus 9 is 14; plus 4 is 18; yes, they add up to 180.
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That means these three angle measures can be the angle measures of a triangle.
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This one is yes.
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The next one, 45 plus 48 plus the 95.
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5 plus... you can add this 5.
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5 plus 5 is 10; plus 8 is 18; put up the 1; 8.
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Already I know that it is not going to add up to 180
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because the last digit has to be 0 and it is not.
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This is 1 plus 4 is 5; plus 4 is 9; that plus 9 is 18.
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This is 188; this is too much.
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That means it can't be the angles of a triangle; this one is no.
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Remember the angles of a triangle have to add up to 180.
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The third example, find X.
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We want to find the measure of this angle right here.
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I have this triangle.
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Remember all three angles of a triangle have to add up to 180.
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But this one is what I am looking for; this is the missing angle measure.
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I don't have this angle measure either.
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If I need to find the third angle measure, I need to have the other two.
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I have this one; I need to have this one also.
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If I don't have this, then I don't know how many goes here.
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I need to find this one first.
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I have to use another method to find this angle measure.
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I know that this right here, this straight line...
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This is from the last lesson, the previous lesson on angles and lines.
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If this is the line here, this one doesn't have an arrow.
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Just do that; here is where it goes up.
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Remember this, two angles right here, they are adjacent angles.
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But they are also supplementary because it is a straight line.
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It is straight; a straight line has an angle measure of 180.
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This whole thing together is 180; that means this one plus this one is 180.
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This is given that it is 135 degrees.
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If this one together with this small one is 180, then I can just subtract it.
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180 minus the 135 to see what this angle measure is going to be.
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180 minus 135; this is going to be 45 degrees.
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That means this has to be 45 because again this angle with this angle together forms a straight line.
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That has to be 180; they are supplementary angles.
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Now that I found this angle and I have this angle, I need to find the measure of this angle.
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I can just say that X... this is just angle measure so I can just leave it as X.
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I don't have to say measure of angle X because that is not a name.
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That is the number of degrees.
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X degrees plus 53 degrees plus 45 degrees all add up to 180 degrees.
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See how they are all in degrees.
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Again I am going to add these two together to see how many of the 180 I am using up.
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Then see how many are left over to be X.
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This is 53 plus 45 is 98 degrees.
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That means X degrees, this many degrees, plus 90 degrees together is 180 degrees.
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Again I am going to subtract this from 98; I get 82 degrees.
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Right here, X is 82 degrees; this has to be 82.
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That way this plus this plus this, the three angles of a triangle, are going to add up to 180.
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That is it for this lesson; thank you for watching Educator.com.