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)
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.
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°
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°.
no each x equals 1
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°.
no its 1x+1x+1x
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.
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)
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.