Use the triangle angle sum theorem to find the measure of the angles for the triangle in the diagram
A 4x+14
C 6x-3
5x+4
According to the triangle angle sum theorem, the sum of the angles in any triangle is always 180 degrees.
So, we can set up the equation:
4x + 14 + 6x - 3 + 5x + 4 = 180
Combining like terms, we have:
15x + 15 = 180
Subtracting 15 from both sides:
15x = 165
Dividing both sides by 15:
x = 11
Now, we can plug in the value of x to find the measure of each angle:
A = 4x + 14 = 4(11) + 14 = 44 + 14 = 58 degrees
C = 6x - 3 = 6(11) - 3 = 66 - 3 = 63 degrees
B = 5x + 4 = 5(11) + 4 = 55 + 4 = 59 degrees
Therefore, the measures of the angles in the triangle are:
A = 58 degrees,
C = 63 degrees,
B = 59 degrees.