Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram. 8x+5 on one side, 5x-1 on the side, and 4x+6 on the bottom
A. 46°, 50°, and 85°
B. 42°, 44°, and 79°
C. 46°, 49°, and 85°
D. 50°, 54°, and 93°
To use the Triangle Angle Sum Theorem, we need to know that the sum of the angles in any triangle is always 180 degrees.
Let's set up an equation using the given information.
The measure of the angle on the left side of the triangle is 8x+5 degrees.
The measure of the angle on the right side of the triangle is 5x-1 degrees.
The measure of the angle on the bottom of the triangle is 4x+6 degrees.
According to the Triangle Angle Sum Theorem, the sum of these three angles equals 180 degrees:
(8x+5) + (5x-1) + (4x+6) = 180
Combine like terms:
17x + 10 = 180
Subtract 10 from both sides:
17x = 170
Divide by 17:
x = 10
Now we can find the measures of each angle by substituting x=10 into the expressions:
The measure of the angle on the left side = 8x+5 = 8(10)+5 = 85 degrees
The measure of the angle on the right side = 5x-1 = 5(10)-1 = 49 degrees
The measure of the angle on the bottom = 4x+6 = 4(10)+6 = 46 degrees
So the measures of each angle in the triangle are: 46°, 49°, and 85°.
Therefore, the answer is C. 46°, 49°, and 85°.