By interior angles theorem, that the sum of the interior angles of a triangle is 180 degrees. So the possible angle C can be calculated by the formula
180 = a + b + c
(180 – 25 – 57) < c < ( 180 – 25 – 51)
98 < c < 104 is the possible measure of angle c
Answer: ∠C is greater than 98⁰ but less than 104⁰.
Step-by-step explanation:
Since we have given that
∠A = 25⁰
And 51⁰ < ∠B < 57⁰
As we know the interior angles theorem which states that "Sum of three angles in a triangle is 180⁰ "
So, According to question,
[tex]\anlge A+\angle B+\angle C=180\textdegree\\\\25+\angle B+\angle C=180\textdegree\\\\\angle B+\angle C=180\textdegree-25\textdegree\\\\\angle B+\angle C=155\textdegree\\\\so,\\\\155\textdegree-57\textdegree<\angle C<155\textdegree-51\textdegree\\\\98\textdegree<\angle C<104\textdegree[/tex]
Hence, ∠C is greater than 98⁰ but less than 104⁰.
