Use the triangle angle sum theorem to find the measures of each angle for the triangle shown in the diagram.
the angles are:
(8x + 5)
(5x - 1)
(4x + 6)
the answers are:
46, 49, and 85
46, 50, and 85
42, 44, and 79
50, 54, and 93
To find the measures of each angle, we will use the triangle angle sum theorem. According to this theorem, the sum of the measures of the angles in a triangle is always 180 degrees.
Therefore, we can set up the following equation:
(8x + 5) + (5x - 1) + (4x + 6) = 180
Simplifying the equation, we get:
17x + 10 = 180
Subtracting 10 from both sides:
17x = 170
Dividing both sides by 17:
x = 10
Now, we can substitute x = 10 back into the expressions for the angles to find their measures:
Angle 1: 8x + 5 = 8(10) + 5 = 85
Angle 2: 5x - 1 = 5(10) - 1 = 49
Angle 3: 4x + 6 = 4(10) + 6 = 46
Therefore, the measures of the angles in the triangle are 85, 49, and 46. Thus, the correct answer is 46, 49, and 85
you sure
Apologies for the confusion. Let's reassess the calculations:
Angle 1: 8x + 5 = 8(10) + 5 = 85
Angle 2: 5x - 1 = 5(10) - 1 = 49
Angle 3: 4x + 6 = 4(10) + 6 = 46
Therefore, the measures of the angles in the triangle are 85, 49, and 46. Thus, the correct answer is 46, 49, and 85.
The angles of a triangle measure (x + 10) , (x + 20) , and (x + 30) . Find the measure of the smallest angle.
answers:
50
60
40
70
To find the measure of the smallest angle, we need to compare the expressions (x + 10), (x + 20), and (x + 30) and determine which one represents the smallest angle.
To do so, we can set the expressions greater than zero and solve for x:
x + 10 > 0
x + 20 > 0
x + 30 > 0
Subtracting the respective constant terms from both sides, we get:
x > -10
x > -20
x > -30
Since we want to find the smallest angle, we need to determine the smallest possible value for x that satisfies all three inequalities. The smallest value that satisfies all three is x > -10.
Let's substitute x = -9 into the expressions to check:
(x + 10) = (-9 + 10) = 1
(x + 20) = (-9 + 20) = 11
(x + 30) = (-9 + 30) = 21
Therefore, when x = -9, the smallest angle measures 1.
Thus, the correct answer is 50.
Use the triangle angle sum theorem to find the measures of each angle for the triangle shown in the diagram.
the angles are:
5x + 4
4x + 14
6x - 3
the answers are:
57, 54, and 69
59, 63 and 48
59, 58, and 63
54, 44, and 82.
To find the measures of each angle in the triangle, we will use the triangle angle sum theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.
Therefore, we can set up the following equation:
(5x + 4) + (4x + 14) + (6x - 3) = 180
Simplifying the equation, we get:
15x + 15 = 180
Subtracting 15 from both sides:
15x = 165
Dividing both sides by 15:
x = 11
Now, we can substitute x = 11 back into the expressions for the angles to find their measures:
Angle 1: 5x + 4 = 5(11) + 4 = 59
Angle 2: 4x + 14 = 4(11) + 14 = 58
Angle 3: 6x - 3 = 6(11) - 3 = 63
Therefore, the measures of the angles in the triangle are 59, 58, and 63. Thus, the correct answer is 59, 58, and 63.