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.
enter just the numbers with a space in between and no commas
To find the value of c, we can set up an equation with the sum of the angles in a triangle:
(8c + 10) + (3c - 20) + (5c + 30) = 180
Combine like terms:
16c + 20 = 180
Subtract 20 from both sides:
16c = 160
Divide by 16:
c = 10
Now we can substitute the value of c back into the expressions for the angles:
First angle: 8c + 10 = 8(10) + 10 = 90 degrees
Second angle: 3c - 20 = 3(10) - 20 = 10 degrees
Third angle: 5c + 30 = 5(10) + 30 = 80 degrees
The measures of the three angles are 90 degrees, 10 degrees, and 80 degrees respectively.
Therefore, the answer is 90 10 80.