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

Question

(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

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°.

Answer 2

Correct 👍

Answer 3

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 4

Yw and have a blissful 😇 day

Answer 5

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 😇