The sum of the angles in a triangle is 180 degrees. Therefore, we have the equation:
(2x+6) + (3x+14) + angle3 = 180
Simplifying the equation, we get:
5x + 20 + angle3 = 180
Subtracting 20 from both sides, we have:
5x + angle3 = 160
Since angle3 is the last missing angle, we can solve for it by subtracting the sum of the other two angles from 180:
angle3 = 180 - [(2x+6) + (3x+14)]
Simplifying:
angle3 = 180 - 2x - 6 - 3x - 14
angle3 = 160 - 5x
So, the measure of the missing angle (angle3) in the triangle is 160 - 5x degrees.
A right triangle has acute angles measuring (2x+6) degrees and (3x+14) degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.
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