Answer-
The values of x and y are 20° and 30, respectively.
Solution-
As in the given triangle all the angles are same so it must a equilateral triangle.
In an equilateral triangle all the measurements of the angles and side length are same. The measurement of the angels are 60°.
As given in the question one side length is 46, so all the side length are same.
So,
[tex]\Rightarrow y+16=46\\\\\Rightarrow y=46-16\\\\\Rightarrow y=30[/tex]
We know that an exterior angle of a triangle is equal to the sum of the opposite interior angles. 80° is the exterior angle opposite to x and one angle of triangle at the top vertex.
[tex]\Rightarrow 80^{\circ}=x+60^{\circ}[/tex]
[tex]\Rightarrow x=80^{\circ}-60^{\circ}[/tex]
[tex]\Rightarrow x=20^{\circ}[/tex]
Therefore, the values of x and y are 20° and 30, respectively.
