Question

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
Skip to navigation

Answer 1

To find the measures of the angles in triangle \( ABC \) using the Triangle Angle Sum Theorem, we start by setting up the equation based on the given expressions for the angles:

\[
\text{Angle } A = 4x + 14, \quad \text{Angle } B = 5x + 4, \quad \text{Angle } C = 6x - 3
\]

According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is 180 degrees:

\[
(4x + 14) + (5x + 4) + (6x - 3) = 180
\]

Now combining like terms:

\[
4x + 5x + 6x + 14 + 4 - 3 = 180
\]
\[
15x + 15 = 180
\]

Next, we solve for \( x \):

\[
15x = 180 - 15
\]
\[
15x = 165
\]
\[
x = \frac{165}{15} = 11
\]

Now, substituting \( x = 11 \) back into the expressions for the angles:

\[
\text{Angle } A = 4(11) + 14 = 44 + 14 = 58
\]
\[
\text{Angle } B = 5(11) + 4 = 55 + 4 = 59
\]
\[
\text{Angle } C = 6(11) - 3 = 66 - 3 = 63
\]

Thus, the angles of triangle \( ABC \) are:

\[
58^\circ, 59^\circ, \text{ and } 63^\circ
\]

The correct option is:

**59°, 58°, and 63°**.