Find x and y.

a) x = 45°, y = 10.9√2

b) x = 45°, y = 10.9

c) x = 30°, y = 10.9

d) x = 30°, y = 10.9√2

Step-by-step explanation:

By the definition of a square, all the sides are the same.  Our figure is marked as such.  Because of this characteristic, that congruency makes the top segment of the square parallel to the bottom segment.  That makes x and the vertex (top) angle in the triangle on the right congruent (these are called alternate interior angles and they are congruent when they lie on opposite sides of a transversal that cuts a pair of parallel lines).  

Also, due to the nature of this type of triangle which is an isosceles triangle, both the acute angles in each triangle are congruent and the other angle is a right angle.  The Pythagorean Triple for the sides in this type of triangle, which is a 45-45-90, is, from shortest side to longest side, (x, x, x√2).  That means that x is a 45 degree angle.

To find the value of y, we use the Pythagorean Triple.  If the side is 10.9, then the hypotenuse is 10.9√2

Choice A is the one you want.