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°, 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 can set up an equation using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.

Let's set up the equation:

angle a + angle b + angle c = 180

(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, substitute the value of x back into the angles:

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 for the triangle in the diagram is 58 degrees, 59 degrees, and 63 degrees.