Use the image to answer the question.
A triangle a b c is shown with angle a measuring 4 x plus 14, angle b measuring 5 x plus 4, and angle c measuring 6 x minus 3.
Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.
(1 point)
Responses
57°, 54°, and 69°
57 degrees , 54 degrees , and 69 degrees
59°, 63°, and 48°
59 degrees , 63 degrees , and 48 degrees
59°, 58°, and 63°
59 degrees , 58 degrees , and 63 degrees
54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees
The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.
Given the angles in the triangle:
angle a = 4x + 14
angle b = 5x + 4
angle c = 6x - 3
We can set up an equation to represent the sum of the angles:
(4x + 14) + (5x + 4) + (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 the value of x back into the expressions for the angles:
angle a = 4(11) + 14 = 58
angle b = 5(11) + 4 = 59
angle c = 6(11) - 3 = 63
Therefore, the measure of the angles for the triangle in the diagram is 58 degrees, 59 degrees, and 63 degrees.
Answer: 59 degrees, 58 degrees, and 63 degrees.