Find all unknown angle measures in each pair of similar triangles...

Question

Find all unknown angle measures in each pair of similar triangles.

Accepted Answer

Welcome back. I am so glad you're here. We're told for the following pair of similar triangles determine the degree measure of all the unknown angles. We're given a diagram with two triangles. The first triangle is ABC labeled B or angle B is labeled 77 degrees. But angles A and C are not labeled. So we'll have to find those two. Our second triangle, which we're told is similar is TUV. Angle U is me is labeled as 81 degrees and angle V is labeled as 22 degrees but angle T is not labeled. So we'll need to figure out that one. Our answer choices are answer choice A angle A equals degrees. Angle C equals 81 degrees and angle T equals degrees. Answer choice B angle A equals 81 degrees. Angle C equals 22 degrees and angle T equals degrees. Answer choice C angle A equals 61 degrees. Angle C equals 42 degrees and angle T equals degrees. And answer choice D angle A equals 42 degrees. Angle C equals 61 degrees and angle T equals degrees. All right. So when we have two similar triangles, we know that they are going to have angles with the same degree measures. So if we look at the first one, that one has angle B, which is 77 degrees, that means that our triangle tuv is also going to have an angle that is measured at degrees. So looking at angle U that's not 77 degrees angle V, that's not 77 degrees. Thereby the process of elimination angle T is going to be 77 degrees. So that's how we get. Angle T equals 77 degrees. Now, it's just a matter of figuring out for angles A and C which one matches up with angle U and which one matches up with angle V. Now we can look at the side lengths and how large or small the angles look to see which one matches up between angle B and angle A, that's a pretty short side and looking at our second triangle, the short side is between angle T and angle U. So directly below our angle T that is attached to that shorter side is going to be angle you. So therefore angle U is similar to angle A and because angle U measures at 81 degrees angle A also measures at 81 degrees. And that makes sense. Angle A looks like it's very close to being a right angle. Now, the only two that are left are angle C and angle V. And that makes sense. Both of the sides attached to angle C are pretty long and that's a pretty small angle. So if angle C equals the degrees, that angle V equals, then that makes sense. So we look at our answer choices for angle A equals 81 degrees. Angle C equals 22 degrees and angle T equals degrees. And that matches with answer choice B well done. We'll catch you on the next one.

Find all unknown angle measures in each pair of similar triangles.

Key Concepts

Similar Triangles

Angle Relationships

Proportionality of Sides

Watch next