Question

it is the 3 enequalites i listed before the question are in the triangle

Answer 1

Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram. (1 point) Responses 54°, 44°, and 82° 54 degrees , 44 degrees , and 82 degrees 59°, 58°, and 63° 59 degrees , 58 degrees , and 63 degrees 59°, 63°, and 48° 59 degrees , 63 degrees , and 48 degrees 57°, 54°, and 69°

Answer 2

To determine if the three inequalities hold for a triangle, we need to consider the lengths of its sides. The inequalities are as follows:

1. Triangle Inequality: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Mathematically, for sides of length a, b, and c, the inequality is written as:
a + b > c
b + c > a
c + a > b

2. Triangle Inequality for Angles: The sum of the measures of any two angles of a triangle must be greater than the measure of the third angle. Mathematically, for angles with measures A, B, and C, the inequality is written as:
A + B > C
B + C > A
C + A > B

If these inequalities are satisfied for a triangle, then the triangle is valid. If any of the inequalities are not satisfied, then the triangle is not valid.

Answer 3

To use the Triangle Angle Sum Theorem to find the measure of the angles in a triangle, we need to know that the sum of the measures of the interior angles of a triangle is always 180 degrees.

From the given options, the only set of angles that add up to 180 degrees is:
57°, 54°, and 69°. Thus, the measure of the angles for the triangle in the diagram is 57 degrees, 54 degrees, and 69 degrees.