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
57°, 54°, and 69°
57 degrees , 54 degrees , and 69 degrees
54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees
59°, 63°, and 48°
To use the Triangle Angle Sum Theorem, we know that the sum of the three angles in a triangle is always 180 degrees.
Therefore, we can set up the equation:
(4x + 14) + (5x + 4) + (6x - 3) = 180.
Combining like terms, we get:
15x + 15 = 180.
Subtracting 15 from both sides, we have:
15x = 165.
Dividing both sides by 15, we find:
x = 11.
Now, we can substitute x = 11 back into the given expressions for the angles to find their measures.
Angle a = 4x + 14 = 4(11) + 14 = 44 + 14 = 58 degrees.
Angle b = 5x + 4 = 5(11) + 4 = 55 + 4 = 59 degrees.
Angle c = 6x - 3 = 6(11) - 3 = 66 - 3 = 63 degrees.
Therefore, the measures of the angles for the triangle are 59 degrees, 58 degrees, and 63 degrees.