Suppose angle a is 25° and angle b is greater than 51° but less than 57°, what are the possible measurements for angle c?

The picture in the attached figure

we know that
m∠A+m∠B+m∠C=180°-----> by the sum of the internal angles of the triangle is 180 degrees
m∠A=25°

for m∠B=51°
find ∠C
∠C=180-[25+51]---------> m∠C=104°
for m∠B greater than 51°------->  m∠C must be less than 104°

for m∠B=57°
find m∠C
m∠C=180-[25+57]---------> m∠C=98°
for m∠B less than 57°------->  m∠C must be greater than 98°

therefore
98° < m∠C < 104°