Question

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Explanation:

Step1: Solve for \( x \)

The two triangles are congruent (since the sides are marked as equal, indicating SAS congruence). So the corresponding angles \( (2x - 25)^\circ \) and \( (x + 5)^\circ \) are equal.
Set up the equation: \( 2x - 25 = x + 5 \)
Subtract \( x \) from both sides: \( 2x - x - 25 = x - x + 5 \)
Simplify: \( x - 25 = 5 \)
Add 25 to both sides: \( x - 25 + 25 = 5 + 25 \)
Simplify: \( x = 30 \)

Step2: Find the measure of the angle with \( x \)

Substitute \( x = 30 \) into \( (x + 5)^\circ \): \( 30 + 5 = 35^\circ \)

Step3: Solve for \( y \)

The angle \( (y + 28)^\circ \) is equal to the angle we just found (\( 35^\circ \)) because they are corresponding angles (vertical angles or alternate interior angles, depending on the diagram, but since the triangles are congruent, corresponding angles are equal).
Set up the equation: \( y + 28 = 35 \)
Subtract 28 from both sides: \( y + 28 - 28 = 35 - 28 \)
Simplify: \( y = 7 \)

Answer:

\( x = 30 \), \( y = 7 \)