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By the interior angles theorem, if angle a is 25 degrees and angle b is greater than 51 degrees but less than 57 degrees what are the possible measurements for angle c

Verified Answer :

MissPhiladelphia

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,

\(\anlge A+\angle B+\angle C=180\textdegree\\\\25+\angle B+\angle C=180\textdegree\\\\\angle B+\angle C=180\textdegree-25\textdegree\\\\\angle B+\angle C=155\textdegree\\\\so,\\\\155\textdegree-57\textdegree<\angle C<155\textdegree-51\textdegree\\\\98\textdegree<\angle C<104\textdegree\)

Hence, ∠C is greater than 98⁰ but less than 104⁰.


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