Question

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

Answer 1

Answer: ∠C is greater than 98⁰ but less than 104⁰.

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.

Answer 2

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