three angles are (8x+5), (5x-1), and (4x+6)
Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram
The Triangle Angle Sum Theorem states that the sum of the three angles in a triangle is always 180 degrees.
So, we can write the equation:
(8x+5) + (5x-1) + (4x+6) = 180
Combining like terms:
17x + 10 = 180
Solving for x:
17x = 180 - 10
17x = 170
x = 170/17
x = 10
Now, substitute x = 10 back into each angle expression:
Angle 1 = 8x + 5 = 8(10) + 5 = 85 degrees
Angle 2 = 5x - 1 = 5(10) - 1 = 49 degrees
Angle 3 = 4x + 6 = 4(10) + 6 = 46 degrees
Therefore, the measures of the three angles are:
Angle 1 = 85 degrees
Angle 2 = 49 degrees
Angle 3 = 46 degrees
The angles of a triangle measure (x+10)° , (x+20)° , and (x+30)° . Find the measure of the smallest angle
To find the measure of the smallest angle, we need to find the value of x that minimizes the expression (x+10)°.
We can set up the following inequality:
x + 10 < x + 20 and solve for x.
Subtracting x from both sides, we get:
10 < 20
As this inequality is true for all values of x, there is no constraint on x that minimizes the expression (x+10)°. Therefore, the smallest angle can be any value greater than 10 degrees, depending on the value of x.
In other words, the measure of the smallest angle is x + 10 degrees.
The angles of a triangle measure (x+10)° , (x+20)° , and (x+30)° . Find the measure of the smallest angle.(1 point)
Responses
50°
50 degrees
40°
40 degrees
70°
70 degrees
60°
To find the measure of the smallest angle, we need to find the value of x that minimizes the expression (x+10)°.
Let's analyze the expressions:
Angle 1: (x+10)°
Angle 2: (x+20)°
Angle 3: (x+30)°
To find the smallest angle, we need to find the smallest value among the expressions (x+10)°, (x+20)°, and (x+30)°.
If we analyze the equations, we can see that as x increases, the expressions (x+10)°, (x+20)°, and (x+30)° also increase.
Therefore, to find the smallest angle, we need to find the smallest value of x. In this case, the smallest value of x will make the expression (x+10)° the smallest among the angles.
Since there is no additional information given regarding the value of x, we cannot determine the exact measure of the smallest angle. The smallest angle will be (x+10)°, with an unknown value depending on the value of x.