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)

Question

the answers are
1. 46 50 and 85
2. 42 44 and 79
3. 46 49 and 85
4.50 54 and 93

Answer 1

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.