The measure of one angle in a triangle is 8c+10 degrees, and the third angle is 5c+30 degrees. Find the value of c and the measures of all three angles.

Answer 1

To find the value of c, we can set up an equation using the fact that the sum of the angles in a triangle is always 180 degrees.

So, we have:

8c + 10 + 5c + 30 + (third angle) = 180

Combining like terms, we get:

13c + 40 + (third angle) = 180

Now, we know that the third angle is equal to 180 degrees minus the sum of the other two angles. So, we can substitute this in:

13c + 40 + (180 - (8c + 10 + 5c + 30)) = 180

13c + 40 + (180 - 13c - 40) = 180

13c + 40 + 180 - 13c - 40 = 180

13c + 140 = 180

13c = 40

c = 40/13

c = 3.0769 (rounded to four decimal places)

Now that we have the value of c, we can substitute it back into the expressions for the angles to find their measures:

Angle 1 = 8(3.0769) + 10 = 34.6154 degrees

Angle 2 = 5(3.0769) + 30 = 45.3846 degrees

Angle 3 = 180 - Angle 1 - Angle 2 = 100 degrees

Therefore, the measures of the three angles are 34.6154 degrees, 45.3846 degrees, and 100 degrees.