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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

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

46°, 50°, and 85°
46 degrees , 50 degrees , and 85 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 given the expressions for the angles, we can use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180 degrees.

Given:

• 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 the terms: \[ 5x + 8x + 4x - 1 + 5 + 6 = 180 \] \[ 17x + 10 = 180 \]

Subtracting 10 from both sides: \[ 17x = 170 \]

Dividing by 17: \[ x = 10 \]

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

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: \[ 4x + 6 = 4(10) + 6 = 40 + 6 = 46° \]

Now we have the measures of the angles:

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

Thus, the measures of the angles are 46°, 49°, and 85°.

The correct response is: 46°, 49°, and 85°.