Question

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°


The image shows a triangle with three letters. At the top of the triangle is the letter B with the equation: 5x+4 right next to it. At the bottom left corner of the triangle, is the letter A with the equation: 4x+14 right next to it. At the bottom right corner of the triangle, is the letter C with the equation: 6x-3 right next to it.

Answer 1

Correct 👍

Answer 2

Bc I’m so happy and awesome I’ll give you guys the answers:

1. 87 degrees
2. 49 degrees
3. 46°, 49°, and 85°
4. 50 degrees
5. 59°, 58°, and 63°

Answer 3

Yw and have a blissful 😇 day

Answer 4

Oh BTW I’m going to give the answers for the Triangle Inequality Theorem quick check:

1. 15
2. 5
3. 9
4. 2 ,7, 6
5. 5.5

Pls have a great day 😇

Answer 5

To find the measures of the angles in the triangle using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees, we can start by setting up the equations based on the angles given.

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

According to the Triangle Angle Sum Theorem:
\[
\text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ
\]
Substituting the expressions for each angle:
\[
(4x + 14) + (5x + 4) + (6x - 3) = 180
\]

Now, combine like terms:
\[
4x + 5x + 6x + 14 + 4 - 3 = 180
\]
\[
15x + 15 = 180
\]

Next, subtract 15 from both sides:
\[
15x = 165
\]

Now, divide by 15:
\[
x = 11
\]

Now that we have the value of \(x\), we can substitute it back into the expressions for each angle to find their measures.

1. Calculate Angle A:
\[
A = 4(11) + 14 = 44 + 14 = 58^\circ
\]

2. Calculate Angle B:
\[
B = 5(11) + 4 = 55 + 4 = 59^\circ
\]

3. Calculate Angle C:
\[
C = 6(11) - 3 = 66 - 3 = 63^\circ
\]

The angles of the triangle are:
- Angle A = \(58^\circ\)
- Angle B = \(59^\circ\)
- Angle C = \(63^\circ\)

Thus, the measures of the angles for the triangle are:
**59°, 58°, and 63°**.