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
54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees
59°, 58°, and 63°
59 degrees , 58 degrees , and 63 degrees
57°, 54°, and 69°
57 degrees , 54 degrees , and 69 degrees
59°, 63°, and 48°
59 degrees , 63 degrees , and 48 degrees
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To find the measures of the angles, we add the three angle measures and set them equal to 180 degrees since it is a triangle.
So, (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, plug x back into each angle measure:
Angle a = 4(11) + 14 = 54 degrees
Angle b = 5(11) + 4 = 59 degrees
Angle c = 6(11) - 3 = 63 degrees
Therefore, the measures of the angles for the triangle are 54°, 59°, and 63°.
So, the correct response is: 59°, 63°, and 48°