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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°, 63°, and 48°
59 degrees , 63 degrees , and 48 degrees
54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees
59°, 58°, and 63°
59 degrees , 58 degrees , and 63 degrees
57°, 54°, and 69°

Answer 1

To find the measure of the angles in the triangle, we use the Triangle Angle Sum Theorem, which states that the sum of the angles in any triangle is always 180°.

We have the following equations:

Angle a = 4x + 14
Angle b = 5x + 4
Angle c = 6x - 3

Now, we can set up an equation using the Triangle Angle Sum Theorem:

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

Combine like terms:

15x + 15 = 180

Subtract 15 from both sides:

15x = 165

Divide both sides by 15:

x = 11

Now, we can substitute x = 11 into the equations for angle measurements:

Angle a = 4(11) + 14 = 58°
Angle b = 5(11) + 4 = 59°
Angle c = 6(11) - 3 = 63°

Therefore, the measure of the angles for the triangle in the diagram is 58°, 59°, and 63°.

The correct response is:
59°, 58°, and 63°