To find the measures of each angle in the triangle, we need to use the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180 degrees.
So, we can set up an equation using the given angle measures:
(8x+5) + (4x+6) + (5x-1) = 180
Combine like terms:
17x + 10 = 180
Subtract 10 from both sides:
17x = 170
Divide by 17:
x = 10
Now that we know the value of x, we can find the measure of each angle:
Angle 1: 8x + 5 = 8(10) + 5 = 80 + 5 = 85 degrees
Angle 2: 4x + 6 = 4(10) + 6 = 40 + 6 = 46 degrees
Angle 3: 5x - 1 = 5(10) - 1 = 50 - 1 = 49 degrees
Therefore, the measures of each angle in the triangle are: 85 degrees, 46 degrees, and 49 degrees.
Triangle Angle Sum Theorem Quick Check
Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.
（8x+5）°. (4x + 6) °. (5x - 1) °
1 answer
1 answer