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.

Question

(1 point)
x =

(Type the number only! No letters or symbols)

Answer 1

Since triangles ABC and XYZ are congruent, the corresponding angles in both triangles are equal. Therefore, we can set up the following equation based on the information provided:

\[ \angle A = \angle X \]

Substituting the values for the angles gives:

\[ 5x + 3 = 7x - 27 \]

Now, we can solve for \( x \):

1. First, rearrange the equation:

\[ 5x + 3 = 7x - 27 \]

2. Subtract \( 5x \) from both sides:

\[ 3 = 2x - 27 \]

3. Add \( 27 \) to both sides:

\[ 30 = 2x \]

4. Divide both sides by \( 2 \):

\[ x = 15 \]

Thus, the value of \( x \) is:

\[ \boxed{15} \]