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
54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees
59°, 63°, and 48°
59 degrees , 63 degrees , and 48 degrees
59°, 58°, and 63°
59 degrees , 58 degrees , and 63 degrees
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To find the measure of the angles for the triangle, we need to set up the equation using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always equal to 180 degrees.
Therefore, we have:
(4x + 14) + (5x + 4) + (6x - 3) = 180
Combine like terms:
15x + 15 = 180
Simplify:
15x = 165
Divide both sides by 15 to solve for x:
x = 11
Now substitute x=11 back into the given equations for each angle 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 measure of the angles for the triangle in the diagram is 58 degrees, 59 degrees, and 63 degrees.