Use the image to answer the question. 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°

Question

Use the image to answer the question. 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°

Angles:
5x+4
4x+14
6x-3

Answer 1

To find the measure of the angles in the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.

We can set up an equation using the given expressions for the angles:

(5x+4) + (4x+14) + (6x-3) = 180

Combine like terms:

15x + 15 = 180

Subtract 15 from both sides:

15x = 165

Divide both sides by 15:

x = 11

Now, we can substitute x = 11 back into the expressions for the angles to find their measures:

Angle 1: 5x+4 = 5(11)+4 = 59 degrees
Angle 2: 4x+14 = 4(11)+14 = 58 degrees
Angle 3: 6x-3 = 6(11)-3 = 63 degrees

Therefore, the measure of the angles for the triangle in the diagram is 59 degrees, 58 degrees, and 63 degrees.