To find the measures of angles A, B, and C in the triangle, we need to use the fact that the sum of the interior angles in any triangle is always $180^\circ$.

Given:

• Angle A = $n + 20^\circ$
• Angle B = $3n - 10^\circ$
• Angle C = $n^\circ$

Now, the equation based on the angle sum property of the triangle is:

$(n + 20^\circ) + (3n - 10^\circ) + n^\circ = 180^\circ$

Step 1: Combine like terms

$n + 3n + n + 20^\circ - 10^\circ = 180^\circ$ $5n + 10^\circ = 180^\circ$

Step 2: Solve for $n$

Subtract $10^\circ$ from both sides: $5n = 170^\circ$ Divide by 5: $n = 34^\circ$

Step 3: Find the measures of each angle

• Angle A: $n + 20^\circ = 34^\circ + 20^\circ = 54^\circ$
• Angle B: $3n - 10^\circ = 3(34^\circ) - 10^\circ = 102^\circ - 10^\circ = 92^\circ$
• Angle C: $n = 34^\circ$

Final answers:

• The measure of angle A is 54 degrees.
• The measure of angle B is 92 degrees.

If you have any further questions or want more details, feel free to ask!

Here are 5 related questions to explore:

1. What would the angles be if $n$ was equal to 40 degrees?
2. Can the values of $n$ create a triangle where all angles are equal?
3. How would the triangle change if the sum of angles was 200 degrees instead?
4. What would be the third angle if angles A and B were provided?
5. How do you calculate the area of a triangle if you know two angles and one side?

Tip: Always double-check your calculations, especially when summing angles in a triangle.