Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram. the diagram has a scalene triangle one angle is (8x+5) the second angle is (5x-1) the third angle is (4x+6)
the answers are
1. 46 50 and 85
2. 42 44 and 79
3. 46 49 and 85
4.50 54 and 93
To find the measures of each angle for the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.
Let's solve for x first:
(8x+5) + (5x-1) + (4x+6) = 180
Combine like terms:
17x + 10 = 180
Subtract 10 from both sides:
17x = 170
Divide both sides by 17:
x = 10
Now substitute x = 10 into the expressions for the angles:
Angle 1: 8(10) + 5 = 85 degrees
Angle 2: 5(10) - 1 = 49 degrees
Angle 3: 4(10) + 6 = 46 degrees
Therefore, the measures of each angle for the triangle are 85 degrees, 49 degrees, and 46 degrees.
So the correct answer is: 3. 46, 49, and 85 degrees.