In congruent triangles ΔXYZ and ΔEGF, corresponding angles and sides are equal: m∠X = m∠G = 107°, m∠Y = m∠F = 48°, and m∠Z = m∠E = 25°.
Sides XY, YZ, and ZX are equal to sides EF, FG, and EG respectively.
The student is asking about finding measurements of unknown sides and angles in congruent triangles in the subject of Mathematics, specifically geometry.
If triangles ΔXYZ and ΔEGF are congruent, then corresponding sides and angles are equal in measure.
Since the sum of the angles in a triangle must equal 180 degrees, we can find m∠Z by subtracting the known angles from 180°:
m∠Z = 180° - m∠Y - m∠X = 180° - 48° - 107° = 25°
Now we know the measure of each angle: m∠X = 107°, m∠Y = 48°, and m∠Z = 25°. Correspondingly, m∠G = 107°, m∠F = 48°, and m∠E = 25°.