The triangles ∆ABC and ∆DEF are similar triangles, and ∆ABC ≅ ∆DEF. The values of x and y are 30.6 and 30° respectively.
Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
We have that line AC of the triangle ∆ABC corresponds to line BK of the triangle ∆DEF and also angle A of the triangle ∆ABC corresponds to angle D of the triangle ∆DEF.
We can evaluate for the values of x and y as follows:
2y - 5 = 65
2y = 65 - 5 {subtract 5 from both sides}
2y = 60
y = 60/2 {divide through by 2}
y = 30
2x + y = 90.6
2x + 30 = 90.6
2x = 90.6 - 30 {subtract 30 from both sides}
2x = 60.6
x = 60.6/2 {divide through by 2}
x = 30.3
In conclusion, the triangles ∆ABC and ∆DEF are similar triangles, and ∆ABC ≅ ∆BMK. The values of x and y are 30.6 and 30° respectively.