The triangle similar to DEF will have an angle that measures 80 degrees, an angle that measures 55 degrees, and an angle that measures 45 degrees.
Similarity of Triangles
Two triangles are considered to be similar if their corresponding angles are congruent and sides are in proportion.
How to find angles if two triangles are similar?
The triangle DEF is similar to any other triangle.
Consider the following figure.
So, [tex]100^{o} + x^{o} = 180^{o}[/tex]
[tex]x^{o} = 180^{o} - 100^{o}[/tex]
[tex]x^{o} = 80^{o}[/tex]
Also, [tex]y^{o} +135^{o} = 180^{o}[/tex]
[tex]y^{o} = 180^{o} -135^{o}[/tex]
[tex]y^{o} = 45^{o}[/tex]
The sum of all angles of a triangle is [tex]180^{o}[/tex].
So, angle D + angle E + angle F = [tex]180^{o}[/tex]
That is, [tex]80^{o}+z^{o} + 45^{o}=180^{o}[/tex]
Simplify further
[tex]z^{o} =55^{o}[/tex]
Thus, the triangle similar to DEF will have an angle that measures 80 degrees, an angle that measures 55 degrees, and an angle that measures 45 degrees.
Learn more about the similarity of triangles here-
https://brainly.com/question/25882965
#SPJ2
