Final answer:
The sum of the angle measures of a triangle equation is A + B + C = 180 degrees. For right triangles, the Pythagorean theorem a² + b² = c² is used to relate the lengths of the legs with the hypotenuse. Additional information is needed to find specific values of x and y using these equations.
Step-by-step explanation:
The equation that represents the sum of the angle measures of a triangle is angle A + angle B + angle C = 180 degrees. This is a foundational concept in geometry stating that if you have a three sided figure lying on a plane, the three angles inside that figure will always add up to 180 degrees.
In the context of right triangles, the Pythagorean theorem is also important. It states that the square of the length of the hypotenuse (side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, a² + b² = c², where c is the hypotenuse and a and b are the other two sides.
To find the values of x and y in the context of a right triangle, you would typically be given some additional information about the lengths of the sides or the angles. If given the lengths of two sides, you could use the Pythagorean theorem to solve for the third. If given an angle and one side, you might use trigonometric functions (sine, cosine, tangent) based on the context provided to solve for the unknown values.