Triangles ABC and XYZ are congruent, and the measure of angle A = 5x + 3, the measure of angle B = 3x + 23, and the measure of angle X = 7x - 27. Find the value of x. (1 point)

Answer 1

By the Angle-Side-Angle (ASA) congruence criterion, if triangles ABC and XYZ are congruent, then their corresponding angles are equal.

This means that:

angle A = angle X
angle B = angle Y
angle C = angle Z

Therefore, we have the equations:

5x + 3 = 7x - 27 (equation 1)
3x + 23 = 7x - 27 (equation 2)

Let's solve equation 1 for x:

5x + 3 = 7x - 27

Subtract 5x from both sides:

3 = 2x - 27

Add 27 to both sides:

30 = 2x

Divide both sides by 2:

x = 15

Now, let's check our solution with equation 2:

3x + 23 = 7x - 27

Substituting x = 15:

3(15) + 23 = 7(15) - 27

45 + 23 = 105 - 27

68 = 78

Since the equation is not true for x = 15, the value of x is not valid.

Therefore, there is no solution for x in this problem.