Final answer:
To find each angle's measure in the equation (11n+9) + (n+5) + (7n-5) = 180, we first solve for n, which is 9. Then, we calculate each angle with this value, resulting in angles of 108 degrees, 14 degrees, and 58 degrees, which check out since they add up to 180 degrees.
Step-by-step explanation:
Finding the Angle Measures in a Triangle
When we consider a triangle, we know that the sum of the interior angles in a triangle always adds up to 180 degrees. This is a fundamental rule in geometry. The equation given, (11n+9) + (n+5) + (7n-5) = 180, represents the three angles of a triangle.
Let's solve for n to find the angles:
- Combine like terms: 11n + n + 7n + 9 + 5 - 5 = 180
- Simplify the equation: 19n + 9 = 180
- Subtract 9 from both sides: 19n = 171
- Divide by 19 to solve for n: n = 9
Now let's find the measure of each angle:
- First angle: 11n + 9 which equals 11(9) + 9 = 108 degrees
- Second angle: n + 5 which equals 9 + 5 = 14 degrees
- Third angle: 7n - 5 which equals 7(9) - 5 = 58 degrees
Checking our answer: 108 + 14 + 58 = 180 degrees, which confirms that our answer is reasonable and all three angles add up to 180 degrees as expected for a triangle.