Use the image to answer the question.

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°

Answer 1

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.