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 3 Angles .
The sum of the angles in a triangle is always 180 degrees. So, we can set up the following equation:
(8c+10) + (3c-20) + (5c+30) = 180
Combining like terms, we get:
16c + 20 = 180
Subtracting 20 from both sides, we get:
16c = 160
Dividing both sides by 16, we get:
c = 10
Now, we can substitute this value of c back into the expressions for each angle to find their measures:
First angle = 8c + 10 = 8(10) + 10 = 80 + 10 = 90 degrees
Second angle = 3c - 20 = 3(10) - 20 = 30 - 20 = 10 degrees
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, respectively.