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Hi, this is Julie Harland and I'm your math gal.
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Please visit my website at yourmathgal.com where you could search for any of my videos organized by topic.
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This is part five of solving problems with angles and triangles.
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In this video, we use our knowledge of angles and geometry to find the measure of an angle given a diagram.
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We do three problems. The third one does not involve a triangle, so it just turns knowledge of angles.
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We're going to do this geometry problem. Find the measure of angle a.
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We have to see what's given here. We know this angle over here is 100 degrees.
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Since together this angle over here, it has to add up to 180.
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Remember, these are supplementary angles.
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If we add this angle, we can draw that in.
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What about here? The 105 degrees?
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If we add these two angles together, it has to be 180 degrees.
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That one would have to be 75 degrees.
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If we know two angles in a triangle, we can figure out this third angle over here.
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We know that 80 plus 75 plus, let's just call this x. We know that has to add up to 180 degrees.
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If you want to write an equation to figure that out, you can.
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Some of you can do that in your head.
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We know that we've got, I'm going to make this simple.
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I'm going to subtract 80 from both sides first.
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I get x plus 75.
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Equal of 100 degrees, so x is 25 degrees.
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Of course, you could have added and got x plus 155 and then subtracted 155 from both sides.
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I'm just going to get x equals 25.
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We know this angle here for x is 25 degrees.
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We figured out that that was 25 degrees.
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Now we know what, a plus that 25 has to add up to 180 as well.
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So, a plus 25.
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I'm going to leave off the degree symbol.
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This one in the end, we can write our answer in degrees.
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So, we're going to have to subtract 25 from both sides.
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So, a is 155 degrees.
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Now, here's something interesting you may have noticed.
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This adds up to 155 and this adds up to 155.
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My answer over here is 155.
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That's going to be true because these three angles inside the triangle,
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the interior angles have to add up to 180.
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So, 25 plus these two angles is 180 and 25 plus angle A has to add up to 180.
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So, it makes sense that A really is the same thing as the sum of 80 plus 75.
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In any case, we found the measure of angle A.
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This is 155 and remember to write our answer in degrees.
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Here's another problem for you to try.
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Find the measure of angle B.
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Okay, so hit the video on pause and try this on your own first.
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All right, so we have to see what we know here.
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We know that this is 120 degrees and remember to angle,
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these are called vertical angles right here.
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So, this over here has to also be 120 degrees.
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Now, what do we know about this angle here?
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This is 160.
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It's supplementary with this other angle over here because that forms a straight line.
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So, those have to add up to 180 degrees.
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So, that should be 20 degrees.
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So, I've got 120 degrees and 20 degrees inside this triangle.
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So, what would this third angle be?
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And of course, that third angle will be the same thing as whatever B is, right?
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Because this is a vertical.
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So, if I want, I can even say, well, if this is B, I know inside here, that's also B.
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And these three angles add up to 180.
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So, that's how we could write our equation.
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And there's more than one way of figuring this out.
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This is just one way that came to mind for me.
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So, I've got B plus 140 degrees.
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180 degrees.
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So, track 140 from both sides.
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And we've got these 40 degrees.
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So, the answer, I forgot to say, find the measure of angle B.
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I've got the thing I was looking for.
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So, the answer is, we measure 40 degrees.
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All right, here's another problem.
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Find the measure of angle A.
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See if you could do this one on your own from the information given in this picture.
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All right, what do we have here?
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We have the right angle right here.
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Remember, that means this is 90 degrees.
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That this part is 55 degrees.
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So, we should be able to figure out this part over here.
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You know that 55 plus that angle has to add up to 90 degrees.
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So, what would that be?
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That would be 35 degrees.
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Now, you could write an equation to figure that out first, if you'd like.
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You would say 55 plus X or whatever you want to call it equals 90.
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Notice that these two add up to 90 degrees.
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So, now, how are we going to get angle A?
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Well, these two have to add up to 180.
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So, then, if you want, you could write an equation.
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A plus 35 equals 180.
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I'm leaving off the degrees, but keep in mind at the end.
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Then you have to write that down.
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So, A would be 145.
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So, the answer here is 145 degrees.
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So, we're using our knowledge of geometry about the different angles,
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about the angles in the triangle, etc. to figure out other angles.
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I could have had an angle over here, B, instead, you know, how big is angle B.
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And hopefully, you could do that.
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You know, all together, these two would have to add up to 180, etc.
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So, there's a lot of different questions that could be asked.
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You just have to use your knowledge of what a right triangle is.
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Your knowledge of supplementary angles, to one of the one angle.
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So, they add up to 180 degrees, etc.
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Please visit my website at yourmathgal.com, where you can view all of my videos, which are organized by topic.