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

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

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

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

50°
, 54°
, and 93°

Answer 1

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

Let’s denote the angles as follows:

- Angle A = \( 5x - 1 \)
- Angle B = \( 8x + 5 \)
- Angle C = \( 4x + 6 \)

According to the Triangle Angle Sum Theorem:

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

Combining like terms, we get:

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

This simplifies to:

\[
17x + 10 = 180
\]

Now, we’ll isolate \( x \):

\[
17x = 180 - 10
\]
\[
17x = 170
\]
\[
x = 10
\]

Now that we found \( x \), we can calculate each angle:

1. Angle A:
\[
5x - 1 = 5(10) - 1 = 50 - 1 = 49°
\]

2. Angle B:
\[
8x + 5 = 8(10) + 5 = 80 + 5 = 85°
\]

3. Angle C:
\[
4x + 6 = 4(10) + 6 = 40 + 6 = 46°
\]

Thus, the measures of the angles are:

- Angle A: 49°
- Angle B: 85°
- Angle C: 46°

The final values are:

**46°, 49°, and 85°**

So the correct response is:

**46°, 49°, and 85°**.