the vertex angle of an isosceles triangle measures 40°. what is the measure of a base angle? This is a topic that many people are looking for. bluevelvetrestaurant.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, bluevelvetrestaurant.com would like to introduce to you the vertex angle of an isosceles triangle measures 40° what is the measure of a base angle?. Following along are instructions in the video below:
s ask against the vertex angle of an isosceles triangle measures 40 degrees. What is is the measure of a base triangle. So we have so i like this i this im looking at this first half of our solution.
I like to i like what theyre doing already because they have some type of diagram and with geometry problems. Again you see this problem probably in a geometry class. Or you would see this in a grade 9.
Maybe introduction to trigonometry kind of unit. Kind of problem type of problem. So this here is a great approach to look in this problem.
So we wont ever draw. What we actually want to draw a diagram to help us figure this out so what we can do here is im gonna actually copy their um their diagram here because its the correct diagram so we have is the vertex angle of an isosceles triangle. So the vertex here angle would be this angle.
A because our saucily triangle means that two sides are the same right so remember so no to that and isosceles triangle. Oh. Thats not how you spell triangle.
We have two sides are the same two side lengths. Are the same so we did not do these these guys with a small right so this here means that these two sides are the same and the vertex angle of these isis triangles or where these isosceles triangle would be here because it meets at this angle. Here so this angle would be 40 degrees.
And this is exactly the same diagram.
We have here so this is correct. So we have an isosceles triangle. Where true side lengths are the same and its asking what is the measure of a base angle.
So we want to figure out when this is in blue. What is these angles. Here we usually denote this in theta or some type of greek letter to figure out what the angle is of the base or what is the measure of the base angle.
Here so this problem really breaks down in to our understanding or the fundamental mental understanding of our triangles well isosceles triangle are equal lateral triangle it has acute angles and obtuse angles as well in triangles as well and what we have to know on to solve this problem. What the giveaway here is this triangle being an isosceles triangle. If we know that two satellites are the same.
We know that their angles. Must also be the same due to the theorem. Where you have you have side side side side angle or side side side.
And those theorems in geometry. Let us help us prove that whether something is congruent or similar. Or what not so in this case.
Here an isosceles triangle. If two so i could say if tucson legs are the same are the same then their angles. Must also be the same so that means we know that this angle angle b.
Here and angle c are going to be equal to each other so were solving for the same angle here and theyre not theyre gonna be the same no value here and if we know this piece of information that the problem is very very easy right we know that in a triangle.
We know what the sum of the interior angles in the triangle. Sorry the sum of the interior angles of a triangle. Its going to be a hundred and eighty degrees right so we can say that sum of interior angles in triangle equals 180.
Degrees. Right so therefore we can say well we can say that a hundred and eighty degrees is going to equal our vertex angle. Which is 44 degrees plus plus.
This angle here and this angle. Here. And we know these guys are the same so we can say angle theta plus.
Theta plus theta and we know that thetas are the same right so we can collect like terms you can also visualize this as any type of variable you want you can visualize this as x or what not so you can say 180 degrees or equal 40 degrees plus q. Theta cuz you can collect these like terms right. And what we can easily do now we can easily solve for this data here using algebra right so you can move 40 degrees to the other side and isolate theta here.
So i can subtract 40 from both sides. Here so i would get 180 minus 40. Which is going to be a 104 degrees.
Its going to even equal to theta and then finally i could divide both sides by 2 right so theta here is going to equal 140 degrees. Divided by 2 that will equal 70 degrees. So therefore we can say that this angle.
Here is going to be 70 degrees.
And this angle here is also equal 70 degrees. And you can make sure that they add up to 180 degrees. Right 70 degrees plus 70.
Degrees. Is 140 plus 40. Degrees.
Here is 180. So. This here.
Is our solution for this problem. So you can stay there for base angle. Equals 70.
Degrees. And this here is our solution for this problem. So lets check the solution.
So it says since abc is an isosceles triangle in which side a b is equal to ec this implies that angle b equals angle z. So this is the correct this is the current they use the correct theorem here. And again.
You simply just have to isolate for that theta and i chose using theta that you chose using angle b. Which is totally fine and this here is going to equal 70 degrees. So this solution here is correct music.
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