Suppose Angle A is 25° and Angle B is greater than 51° but less than 57°, what are the possible measurements for Angle C?
Responses
A 73 < C < 104
73 < C < 104
B 98 < C < 12998 < C < 129
C 98 < C < 10498 < C < 104
D 123 < C < 129
B 98 < C < 129
why
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.
To find the possible measurements for Angle C, we need to consider the relationship between the three angles in a triangle. The sum of the interior angles in a triangle is always 180°.
We know that Angle A is 25° and Angle B is greater than 51° but less than 57°.
To find the possible measurements for Angle C, we can subtract the sum of angles A and B from 180°.
180° - 25° - 57° = 98°
So, the possible measurements for Angle C are greater than 98° but less than 180°.
Out of the given options, the correct answer is:
B) 98 < C < 129