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.
The sum of the angles in a triangle is always 180 degrees.
So,
(8c + 10) + (3c - 20) + (5c + 30) = 180
Combining like terms, we have:
8c + 10 + 3c - 20 + 5c + 30 = 180
16c + 20 = 180
Subtracting 20 from both sides, we get:
16c = 160
Dividing both sides by 16, we find:
c = 10
Now, we can substitute this value of c into the expressions for each angle:
The first angle:
8c + 10 = 8(10) + 10 = 80 + 10 = 90 degrees
The second angle:
3c - 20 = 3(10) - 20 = 30 - 20 = 10 degrees
The third angle:
5c + 30 = 5(10) + 30 = 50 + 30 = 80 degrees
So, the value of c is 10, and the measures of the three angles are 90 degrees, 10 degrees, and 80 degrees.