Answer:
x = [tex]2\sqrt7[/tex]
y = [tex]2\sqrt7[/tex]
Step-by-step explanation:
Hello!
This is a right isosceles triangle (45°-45°-90°). You can solve for the missing angle by simply subtracting 45° and 90° from 180° (sum of angles in a triangle equals 180°)
Since the triangle is isosceles, x and y are congruent because they are the legs opposite to the congruent angles.
In a right isosceles triangle, the hypotenuse is always the measure of one leg multiplied by [tex]\sqrt2[/tex].
So, let's use leg y, [tex]y\sqrt2 = 2\sqrt{14}[/tex]
Solve for y:
[tex]y\sqrt2 = 2\sqrt{14}\\\\y = $\frac{2\sqrt{14}}{\sqrt2}$\\\\y = 2\sqrt7[/tex]
y = [tex]2\sqrt7[/tex], which means that x is also [tex]2\sqrt7[/tex]
