Remote, Exterior and Interior Angles of A Triangle
That is degrees of rotation. So all your exterior turns are added up to degrees. Let us now understand the topic exterior and interior angles of triangles in. An exterior angle of a triangle is an angle formed by one side of the triangle and is equal to the sum of the measures of the two non-adjacent interior angles. Rule 3: Relationship between measurement of the sides and angles in a triangle: The largest interior angle and side are opposite each other. The same rule.
So the first thing you might say-- and this is a general way to think about a lot of these problems where they give you some angles and you have to figure out some other angles based on the sum of angles and a triangle equalingor this one doesn't have parallel lines on it. But you might see some with parallel lines and supplementary lines and complementary lines-- is to just fill in everything that you can figure out, and one way or another, you probably would be able to figure out what this question mark is.
So the first thing that kind of pops out to me is we have one triangle right over here. We have this triangle on the left. And on this triangle on the left, we're given 2 of the angles.
And if you have 2 of the angles in a triangle, you can always figure out the third angle because they're going to add up to degrees. So if you call that x, we know that x plus 50 plus 64 is going to be equal to degrees. Or we could say, x plus, what is this, X plus is equal to degrees. We could subtract from both sides of this equation, and we get x is equal to minus So 80 minus So x is 66 degrees. Now, if x is 66 degrees, I think you might find that there's another angle that's not too hard to figure out.
So let me write it like this. Let me write 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 right over here. Their 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 degrees. And we know x is equal to 66 degrees. So this is And so we can subtract 66 from both sides, and we get y is equal to-- these cancel out-- minus 66 is And that number might look a little familiar to you.
Notice, this was the exact same sum of these 2 angles over here. And that's actually a general idea, and I'll do it on the side here just to prove it to you. If I have, let's say that these 2 angles-- let's say that the measure of that angle is a, the measure of that angle is b, the measure of this angle we know is going to be minus a minus b. That's this angle right over here. And then this angle, which is considered to be an exterior angle.
So in this example, y is an exterior angle.
Triangles Side and Angles
In this example, that is our exterior angle. That is going to be supplementary to minus a minus b. So this angle plus minus a minus b is going to be equal to So if you call this angle y, you would have y plus minus a minus b is equal to You could subtract from both sides.
At the top of our triangle, we have three angles based around our line.Angles in Triangles
Let's label them X, Y and Z. These three angles form a straight line, so they add up to what? The sum of the interior angles of a triangle is degrees. Since we have a parallel line at the bottom of our triangle, we have alternate interior angles. So, the inside angle at the bottom is also equal to X.
Z has an alternate interior angle at the bottom. And look what we did. We just proved that the sum of the interior angles of a triangle is degrees. Practice Problems Okay, so we know that. How can it help us?
Exterior and Interior Angles of Triangle
In a triangle, you can never be stuck with one missing piece. In the triangle we were just looking at above, what if we know that angle X is 35 degrees and angle Z is 60 degrees? Oh, man, if only we know angle Y, we'd know them all. It's - 35 - 60, which is Right triangle for example problem In this one, we know angle X is 53 degrees.
Wait, that's only one angle. We're losing pieces of this puzzle. Is it the cat? Is the cat stealing pieces? See this symbol at the bottom left?
exterior and interior angles of triangle
This means that this angle is 90 degrees. So, we know we have a 53 degree angle and a 90 degree angle. If we subtract 53 and 90 fromwe get 37 degrees.