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
59°, 58°, and 63°
59 degrees , 58 degrees , and 63 degrees
54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees
57°, 54°, and 69°
57 degrees , 54 degrees , and 69 degrees
59°, 63°, and 48°
To find the measures of the angles, set up the equation:
4x + 14 + 5x + 4 + 6x - 3 = 180
Combine like terms:
15x + 15 = 180
Subtract 15 from both sides:
15x = 165
Divide by 15:
x = 11
Now, substitute x back into each angle's expression:
Angle a: 4(11) + 14 = 59 degrees
Angle b: 5(11) + 4 = 59 degrees
Angle c: 6(11) - 3 = 63 degrees
Therefore, the measures of the angles are 59°, 59°, and 63°. So, the correct answer is:
59°, 59°, and 63°