Question
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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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
Skip to navigation
Answers
GPT 3.5
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°
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°