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The measure of one angle in a triangle is 8c + 10 degrees, the second angle is 3c - 20 degrees, and the third angle is 5c + 30 degrees. Find the value of c and the measures of all three angles.
To find the value of c, we know that the sum of all interior angles in a triangle is 180 degrees.
So, we can set up the equation:
(8c + 10) + (3c - 20) + (5c + 30) = 180
16c + 20 = 180
16c = 160
c = 10
Now we can substitute c = 10 back into each of the angles to find their measures:
8(10) + 10 = 80 + 10 = 90 degrees
3(10) - 20 = 30 - 20 = 10 degrees
5(10) + 30 = 50 + 30 = 80 degrees
Therefore, the measures of the angles are 90 degrees, 10 degrees, and 80 degrees.