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°
54°, 44°, and 82°
59°, 58°, and 63°
59°, 63°, and 48°
To find the measure of the angles in the triangle, we need to apply the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in any triangle is always 180°.
Let's set up an equation using this information:
(4x + 14) + (5x + 4) + (6x - 3) = 180
Simplifying the equation by combining like terms:
15x + 15 = 180
Subtracting 15 from both sides:
15x = 165
Dividing both sides by 15:
x = 11
Now we can substitute x = 11 into the angles a, b, and c to find their measures:
Angle a = 4x + 14 = 4(11) + 14 = 44 + 14 = 58°
Angle b = 5x + 4 = 5(11) + 4 = 55 + 4 = 59°
Angle c = 6x - 3 = 6(11) - 3 = 66 - 3 = 63°
Therefore, the measure of the angles for the triangle in the diagram is 59°, 58°, and 63°.
The correct answer is:
59°, 58°, and 63°