Question

Given ABC ≅ DEF and m∠A = 3x - 2y, m∠B = 2x, m∠D = 48, m∠E = 2, m∠F = 20x, solve for x and y.

a) x = 14, y = 12
b) x = 8, y = 3
c) x = 12, y = 14
d) x = 3, y = 8

Answer 1

To solve for x and y, set up a system of equations using the given information and the fact that corresponding angles are congruent. Solve the equations to find the values of x and y.

Step-by-step explanation:

To solve for x and y, we can set up a system of equations using the given information: m∠A = 3x - 2y, m∠B = 2x, m∠D = 48, m∠E = 2, and m∠F = 20x. Since ABC ≅ DEF, corresponding angles are congruent, so m∠A = m∠D and m∠B = m∠E. This leads to two equations: m∠A = m∠D = 48 and m∠B = m∠E = 2. Plugging these values into the equations for m∠A and m∠B, we get:

1. 3x - 2y = 48
2. 2x = 2

Solving equation (2) for x, we get x = 1. Substituting this value into equation (1), we can solve for y: 3(1) - 2y = 48 => 3 - 2y = 48 => -2y = 45 => y = -22.5. Therefore, the solution is x = 1 and y = -22.5.