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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

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°.