Two angles are complementary if the sum of their measures is equal to \( 90^{\circ} \). Georgia draws two complementary angles. One of the angles measures \( 15^{\circ} \) more than 2 times the other angle's measure. A. Model with Mathematics Write a system of equations to represent the situation. B. What are the measures of the two angles?

Let the measure of the first angle be \( x \) degrees, and the measure of the second angle be \( y \) degrees. From the information provided, we can set up the following system of equations: 1. \( x + y = 90 \) (since the angles are complementary) 2. \( x = 2y + 15 \) (since one angle measures 15 degrees more than 2 times the other) Now, we can substitute the second equation into the first. Substituting \( x \) from the second equation into the first gives us: \[ (2y + 15) + y = 90 \] Combining like terms results in: \[ 3y + 15 = 90 \] To isolate \( y \), subtract 15 from both sides: \[ 3y = 75 \] Dividing by 3 yields: \[ y = 25 \] Now, we can find \( x \) by substituting \( y \) back into the second equation: \[ x = 2(25) + 15 = 50 + 15 = 65 \] Thus, the measures of the two angles are: - \( x = 65^{\circ} \) - \( y = 25^{\circ} \)