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
59°, 63°, and 48°
59 degrees , 63 degrees , and 48 degrees
54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees
57°, 54°, and 69°
To find the measure of the angles in the triangle, we need to set up an equation using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180°.
So, we have:
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 into the expressions for each angle:
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 correct answer is 59°, 58°, and 63°.