Answer:
B. [tex]x=62[/tex]; [tex]y=30[/tex]
Step-by-step explanation:
We have been given two similar triangles. We are asked to find the value of x and y for the given triangles.
[tex]\Delta SWK\sim \Delta EBT[/tex]
We know that the measure of corresponding angles of two similar triangles are equal.
[tex]m\angle S=m\angle E[/tex]
[tex]m\angle W=m\angle B[/tex]
[tex]m\angle K=m\angle T[/tex]
[tex]110=2x-14[/tex]
[tex]2x-14=110[/tex]
[tex]2x-14+14=110+14[/tex]
[tex]2x=124[/tex]
[tex]\frac{2x}{2}=\frac{124}{2}[/tex]
[tex]x=62[/tex]
[tex]m\angle S=m\angle E[/tex]
[tex]40=m\angle E[/tex]
Using angle sum property, we will get:
[tex]m\angle E+m\angle B+m\angle T=180[/tex]
[tex]40+y+110=180[/tex]
[tex]y+150=180[/tex]
[tex]y+150-150=180-150[/tex]
[tex]y=30[/tex]
Therefore, option B is the correct choice.
