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°
, 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°
50 degrees , 54 degrees , and 93 degrees

46°
, 49°
, and 85°
46 degrees , 49 degrees , and 85 degrees
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Answer 1

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

Let the angles be represented as follows:
1. \( A = 5x - 1 \) degrees
2. \( B = 8x + 5 \) degrees
3. \( C = 4x + 6 \) degrees

Now, we set up the equation using the Triangle Angle Sum Theorem:

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

Now, we simplify the left side of the equation:

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

Combining like terms:

\[
(5x + 8x + 4x) + (-1 + 5 + 6) = 180
\]
\[
17x + 10 = 180
\]

Now, we solve for \( x \):

\[
17x = 180 - 10
\]
\[
17x = 170
\]
\[
x = \frac{170}{17} = 10
\]

Now we substitute \( x = 10 \) back into the expressions for the angles:

1. \( A = 5(10) - 1 = 50 - 1 = 49 \) degrees
2. \( B = 8(10) + 5 = 80 + 5 = 85 \) degrees
3. \( C = 4(10) + 6 = 40 + 6 = 46 \) degrees

Therefore, the measures of the angles are:
- \( 49^\circ \)
- \( 85^\circ \)
- \( 46^\circ \)

Looking at the responses, this corresponds to:

**46°, 49°, and 85°**

So the correct answer is:

**46°, 49°, and 85°**.