Answer:
y=10, x=10[tex]\sqrt{2}[/tex]
Step-by-step explanation:
We know that the sum of angles in a triangle is equal to 180, we are given two angles so we just need to find the third. 45+90+x=180 -> x+135=180 -> x=45. From this, we know that the two base angles are equivalent making this triangle an isosceles triangle by base angles theorem. In an isosceles triangle, the two side lengths are the same witch gives us the length of y, because one of the side lengths was given we know that y is equal to that and in this case, it is 10. In a 45-45-90 right triangle, the hypotenuse will always be equal to the side length multiplied by [tex]\sqrt{2}[/tex]. With this we can figure out the length of the final side witch would be 10[tex]\sqrt{2}[/tex]
