Question

Use the image to answer the question.

A triangle is shown with its angles measuring left parenthesis 5 x minus 1 right parenthesis degrees, left parenthesis 8 x plus 5 right parenthesis degrees, and left parenthesis 4 x plus 6 right parenthesis degrees.

Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.

(1 point)
Responses

46°
, 49°
, and 85°
46 degrees , 49 degrees , and 85 degrees

46°
, 50°
, and 85°
46 degrees , 50 degrees , and 85 degrees

42°
, 44°
, and 79°
42 degrees , 44 degrees , and 79 degrees

50°
, 54°
, and 93°

Answer 1

To find the measures of each angle in the triangle, we will use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle equals 180 degrees.

The angles of the triangle are given as:
1. \( (5x - 1)^\circ \)
2. \( (8x + 5)^\circ \)
3. \( (4x + 6)^\circ \)

We can set up the equation:

\[
(5x - 1) + (8x + 5) + (4x + 6) = 180
\]

Now let's combine like terms:

\[
5x + 8x + 4x - 1 + 5 + 6 = 180
\]

\[
(5x + 8x + 4x) + (-1 + 5 + 6) = 180
\]

\[
17x + 10 = 180
\]

Now, we will isolate \( x \):

\[
17x = 180 - 10
\]

\[
17x = 170
\]

\[
x = \frac{170}{17} = 10
\]

Now we will substitute \( x = 10 \) back into each angle:

1. First angle:
\[
5x - 1 = 5(10) - 1 = 50 - 1 = 49^\circ
\]

2. Second angle:
\[
8x + 5 = 8(10) + 5 = 80 + 5 = 85^\circ
\]

3. Third angle:
\[
4x + 6 = 4(10) + 6 = 40 + 6 = 46^\circ
\]

Hence, the measures of each angle are \( 49^\circ \), \( 85^\circ \), and \( 46^\circ \).

Therefore, the correct response is:

**46°, 49°, and 85°**