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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.
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2 points
To find the value of c, we know that the sum of the angles in a triangle is always 180 degrees.
So, we can set up an equation:
(8c + 10) + (3c - 20) + (5c + 30) = 180
Simplifying the equation:
16c + 20 = 180
Subtracting 20 from both sides:
16c = 160
Dividing both sides by 16:
c = 10
Now that we know the value of c, we can substitute it back into the original expressions to find the measures of the angles.
Angle 1: 8c + 10 = 8(10) + 10 = 90 degrees
Angle 2: 3c - 20 = 3(10) - 20 = 10 degrees
Angle 3: 5c + 30 = 5(10) + 30 = 80 degrees
Therefore, c = 10 and the measures of the angles are 90 degrees, 10 degrees, and 80 degrees.