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.
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.
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