Question

Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram. isocles angle a 4x+14 b 5x+4 c 6x-3

(1 point)
Responses

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

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

59°
59
°
, 63°
63
°
, and 48°
48
°
59 degrees , 63 degrees , and 48 degrees

54°
54
°
, 44°
44
°
, and 82

Answer 1

To find the measures of the angles in the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180 degrees.

Given the angles:
- Angle A = \(4x + 14\)
- Angle B = \(5x + 4\)
- Angle C = \(6x - 3\)

We will set up the equation based on the Triangle Angle Sum Theorem:

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

Combining like terms:

\[
4x + 5x + 6x + 14 + 4 - 3 = 180
\]

\[
15x + 15 = 180
\]

Now, we will isolate \(x\) by subtracting 15 from both sides:

\[
15x = 180 - 15
\]

\[
15x = 165
\]

Now, divide by 15:

\[
x = 11
\]

Now, we can substitute \(x = 11\) back into the expressions for each angle:

Angle A:

\[
4x + 14 = 4(11) + 14 = 44 + 14 = 58°
\]

Angle B:

\[
5x + 4 = 5(11) + 4 = 55 + 4 = 59°
\]

Angle C:

\[
6x - 3 = 6(11) - 3 = 66 - 3 = 63°
\]

Now we have the three angles:

- Angle A = 58°
- Angle B = 59°
- Angle C = 63°

The measures of the angles are:
- 58°, 59°, and 63°.

Thus, the correct response is:
**59° , 58° , and 63°**.