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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

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

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

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

46°
, 50°
, and 85°

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.

The angles are given as:

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

Setting up the equation using the Triangle Angle Sum Theorem:

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

Now, combine like terms:

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

Next, subtract \(10\) from both sides:

\[ 17x = 170 \]

Now, divide by \(17\):

\[ x = 10 \]

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

1. First angle: \[ 5x - 1 = 5(10) - 1 = 50 - 1 = 49 \text{ degrees} \]

2. Second angle: \[ 8x + 5 = 8(10) + 5 = 80 + 5 = 85 \text{ degrees} \]

3. Third angle: \[ 4x + 6 = 4(10) + 6 = 40 + 6 = 46 \text{ degrees} \]

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

Thus, the answer that matches the calculated angles is: 46°, 49°, and 85°.