Question

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)
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:

\[
\boxed{15}
\]