Use the image to answer the question.
A triangle a b c is shown with angle a measuring 4 x plus 14, angle b measuring 5 x plus 4, and angle c measuring 6 x minus 3.
Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.
The Triangle Angle Sum Theorem states that the sum of the measures of the interior angles of a triangle is always 180 degrees.
Given that angle a measures 4x + 14, angle b measures 5x + 4, and angle c measures 6x - 3, we can write the equation:
(4x + 14) + (5x + 4) + (6x - 3) = 180
Combining like terms, we get:
15x + 15 = 180
Subtracting 15 from both sides:
15x = 165
Dividing both sides by 15:
x = 11
Now, we can substitute x = 11 back into the expressions for the angles to find their measures.
Angle a = 4x + 14 = 4(11) + 14 = 44 + 14 = 58 degrees
Angle b = 5x + 4 = 5(11) + 4 = 55 + 4 = 59 degrees
Angle c = 6x - 3 = 6(11) - 3 = 66 - 3 = 63 degrees
Therefore, the measure of angle a is 58 degrees, angle b is 59 degrees, and angle c is 63 degrees.