Asked by bigepic

Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.

(8x+5)+(5x-1)+(4x+6)
Answered by bigepic
The angles of a triangle measure (x+10)°, (x+20)°, and (x+30)°. Find the measure of the smallest angle.(1 point)
Responses

40°
40 degrees

50°
50 degrees

70°
70 degrees

60°
Answered by bigepic
no each x equals 1
Answered by bigepic
no its 1x+1x+1x
Answered by bigepic
Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.

(5x+4)+(4x+14)+(6x-3)
Answered by bigepic
to all who see this: the answer for 4 is 50 degrees (triangle sum theorem quick check)
Answered by GPT 3.5
To find the measures of each angle, we need to apply the Triangle Angle Sum Theorem, which states that the sum of the three interior angles of a triangle is always 180 degrees.

So, we add up the measures of the three angles:

(8x+5)+(5x-1)+(4x+6) = 180

Combining like terms:

17x + 10 = 180

Subtracting 10 from both sides:

17x = 170

Dividing both sides by 17:

x = 10

Now, substitute x = 10 back into the expressions for each angle to find their measures:

First angle: 8x + 5 = 8(10) + 5 = 80 + 5 = 85 degrees
Second angle: 5x - 1 = 5(10) - 1 = 50 - 1 = 49 degrees
Third angle: 4x + 6 = 4(10) + 6 = 40 + 6 = 46 degrees

Therefore, the measures of the three angles are 85 degrees, 49 degrees, and 46 degrees.
Answered by GPT 3.5
To find the measure of the smallest angle, we need to find the smallest value among the expressions (x+10)°, (x+20)°, and (x+30)°.

Let's consider the expressions individually:

For (x+10)° to be the smallest, x must be the smallest among the values it can take. Therefore, we need to find the smallest possible value of x.

Since we have no other information given about x, we cannot determine its exact value. However, we can consider a hypothetical scenario in which x takes the smallest possible value, which is x = 0.

Substituting x = 0 into the expressions for the angles:

(x+10)° = (0+10)° = 10°
(x+20)° = (0+20)° = 20°
(x+30)° = (0+30)° = 30°

Therefore, in this hypothetical scenario, the smallest angle measures 10°.

So, the correct answer is 10°.
Answered by GPT 3.5
If each x equals 1, we can substitute x = 1 into the expressions for the angles:

(x+10)° = (1+10)° = 11°
(x+20)° = (1+20)° = 21°
(x+30)° = (1+30)° = 31°

Therefore, when x = 1, the measures of the angles are 11°, 21°, and 31°.

Among these three angles, the smallest angle measures 11°.

So, the correct answer is 11°.
Answered by GPT 3.5
I apologize for the confusion. I misunderstood the given information.

If each angle measures 1x+1x+1x, we can combine like terms to find the measure of the smallest angle.

1x + 1x + 1x = 3x

Therefore, the measure of the smallest angle is 3x.

Since we don't have a specific value for x, we cannot determine the exact measure of the smallest angle. We would need additional information or a specific value for x to calculate the measure.
Answered by GPT 3.5
To find the measures of the angles, we need to apply the Triangle Angle Sum Theorem, which states that the sum of the three interior angles of a triangle is always 180 degrees.

So, we add up the measures of the three angles:

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

Combining like terms:

15x + 15 = 180

Subtracting 15 from both sides:

15x = 165

Dividing both sides by 15:

x = 11

Now, substitute x = 11 back into the expressions for each angle to find their measures:

First angle: 5x + 4 = 5(11) + 4 = 55 + 4 = 59 degrees
Second angle: 4x + 14 = 4(11) + 14 = 44 + 14 = 58 degrees
Third angle: 6x - 3 = 6(11) - 3 = 66 - 3 = 63 degrees

Therefore, the measures of the three angles are 59 degrees, 58 degrees, and 63 degrees.
Answered by GPT 3.5
Apologies for the previous incorrect response. Let's reevaluate the given expression and determine the measure of each angle.

(5x + 4) + (4x + 14) + (6x - 3)

Combining like terms:

15x + 15 = 180

Subtracting 15 from both sides:

15x = 165

Dividing both sides by 15:

x = 11

Now, substitute x = 11 back into the expressions for each angle to find their measures:

First angle: 5x + 4 = 5(11) + 4 = 55 + 4 = 59 degrees
Second angle: 4x + 14 = 4(11) + 14 = 44 + 14 = 58 degrees
Third angle: 6x - 3 = 6(11) - 3 = 66 - 3 = 63 degrees

The measures of the three angles are indeed 59 degrees, 58 degrees, and 63 degrees. I apologize for the confusion.