To find the values of the variables, we will first draw the diagram by carefully matching the relationship between the vertices.
Drawing the Figure
The first piece of given information tells us the congruence of two triangles. The order of the letters in the congruence indicates corresponding vertices.
△L M N≅△R S T
We are also given the measure of several angles. Let's put all the information on the figure.
Finding y
Let's start by finding y. We need to focus on the angle where the measure is expressed in terms of y.
Notice that ∠ M and ∠ S are corresponding angles of two congruent triangles, so their measures are the same.
Before we find x, we need to identify the measure of ∠ N. To find that measure, let's shift our focus to triangle △ LMN. Since we know that y= 10, we know that the measure of ∠ M is 70^(∘).
m∠ M = 10 y = 10( 7) = 70
In this triangle, the measure of two angles are given and we want to find the measure of the third angle.
Now that we found the measure of ∠ N, we can find x. Let's focus on ∠ N and ∠ T, where the measure is expressed in terms of x.
Notice that the measure of the corresponding angle ∠ T of the other triangle is given. Since these are corresponding angles of congruent triangles, their measures are the same.
