Triangle Angle Sum Theorem Quick Check

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Question
Use the image to answer the question.

A triangle a b c is shown with angle a measuring 4 x plus 14, angle b measuring 5 x plus 4, and angle c measuring 6 x minus 3.

Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.

(1 point)
Responses

59°, 58°, and 63°
59 degrees , 58 degrees , and 63 degrees

54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees

57°, 54°, and 69°
57 degrees , 54 degrees , and 69 degrees

59°, 63°, and 48°
59 degrees , 63 degrees , and 48 degrees
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Answer 1

To find the measure of the angles in the triangle using the Triangle Angle Sum Theorem, we need to set up the equation:

angle a + angle b + angle c = 180 degrees

Substituting the given expressions for each angle:

(4x + 14) + (5x + 4) + (6x - 3) = 180

Combining like terms:

15x + 15 = 180

Subtracting 15 from both sides:

15x = 165

Dividing by 15:

x = 11

Now, we can find the measure of each angle by substituting x back into the given expressions:

angle a = 4x + 14 = 4(11) + 14 = 44 + 14 = 58 degrees

angle b = 5x + 4 = 5(11) + 4 = 55 + 4 = 59 degrees

angle c = 6x - 3 = 6(11) - 3 = 66 - 3 = 63 degrees

Therefore, the measure of the angles in the triangle is 59 degrees, 58 degrees, and 63 degrees.
The correct answer is option: 59 degrees , 58 degrees , and 63 degrees.