Suppose Angle A is 25° and Angle B is greater than 51° but less than 57°, what are the possible measurements for Angle C?

Question

Responses

A 73 < C < 104
73 < C < 104

B 98 < C < 12998 < C < 129

C 98 < C < 10498 < C < 104

D 123 < C < 129

Answer 1

B 98 < C < 129

Answer 2

why

Answer 3

The angles inside a triangle add up to 180 degrees. So, we can use the angle sum property of a triangle to find the possible measurements for angle C.

Let's begin by finding the minimum and maximum values for angle B.

Given that angle B is greater than 51° but less than 57°, we have:

51 < B < 57

Now, we can use the angle sum property of a triangle to find the possible measurements for angle C:

C = 180 - (A + B)

Substituting the given values for angle A and the range for angle B, we get:

C = 180 - (25 + B)

C = 155 - B

To find the minimum and maximum values for angle C, we need to substitute the minimum and maximum values for angle B into the formula for angle C:

For the minimum value of angle B (B = 51), we get:

C = 155 - 51 = 104

For the maximum value of angle B (B = 57), we get:

C = 155 - 57 = 98

Therefore, the possible measurements for angle C are:

98 < C < 104.

So, option B is the correct answer.