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)
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.