Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram. 5x + 4 4x + 14 6x - 3
The Triangle Angle Sum Theorem states that the sum of the three angles in a triangle is always 180 degrees.
To find the measure of each angle in the triangle, we need to set up an equation and solve for x.
The three angles in the triangle can be represented by 5x + 4, 4x + 14, and 6x - 3.
Setting up an equation:
(5x + 4) + (4x + 14) + (6x - 3) = 180
Combining like terms:
15x + 15 = 180
Subtracting 15 from both sides:
15x = 165
Dividing both sides by 15:
x = 11
To find the measure of each angle, substitute the value of x back into the expressions:
Angle 1: 5x + 4 = 5(11) + 4 = 55 + 4 = 59 degrees
Angle 2: 4x + 14 = 4(11) + 14 = 44 + 14 = 58 degrees
Angle 3: 6x - 3 = 6(11) - 3 = 66 - 3 = 63 degrees
Therefore, the measure of the angles in the triangle are: 59 degrees, 58 degrees, and 63 degrees.