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, their corresponding angles are equal. Thus, we have:

1. \( \angle A = \angle X \)
2. \( \angle B = \angle Y \)

Given the angles:

• \( \angle A = 5x + 3 \)
• \( \angle B = 3x + 23 \)
• \( \angle X = 7x - 27 \)

Setting \( \angle A \) equal to \( \angle X \):

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

To solve for \( x \), we first isolate \( x \) on one side:

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

\[ 3 = 2x - 27 \]

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

\[ 30 = 2x \]

3. Divide by \( 2 \):

\[ x = 15 \]

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

\[ \boxed{15} \]