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.

Question

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

46°
, 49°
, and 85°
46 degrees , 49 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

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 180 degrees. In this case, we have the angles:

1. \( (5x - 1)^\circ \)
2. \( (8x + 5)^\circ \)
3. \( (4x + 6)^\circ \)

Setting up the equation based on the Triangle Angle Sum Theorem:

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

Now we will combine the terms:

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

Now subtract 10 from both sides:

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

Now, divide by 17:

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

Now that we have the value of \( x \), we can find the angles:

1. \( (5x - 1) = (5(10) - 1) = 50 - 1 = 49^\circ \)
2. \( (8x + 5) = (8(10) + 5) = 80 + 5 = 85^\circ \)
3. \( (4x + 6) = (4(10) + 6) = 40 + 6 = 46^\circ \)

Thus, the measures of the angles are \( 49^\circ, 85^\circ, \) and \( 46^\circ \).

The correct response is:

46°, 49°, and 85°.