Triangle is shown below, with the angle measures as indicated.

Angle A is n plus 20 degrees, angle b is left parenthesis 3 n minus 10 right parenthesis degrees, angle C is n degrees.

What are the measures of and ? Use the drop-down menus to select the correct responses.

The measure of angle A is Query 1
.
The measure of angle B is
values are 3n - 10 and n + 20

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.

Triangle is shown below, with the angle measures as indicated. Angle A is n plus 20 degrees, angle B is (3n - 10) degrees, angle C is n degrees. What are the measures of angles A and B? Use the drop-down menus to select the correct responses.

Learn how to find the measures of angles in a triangle where the angles are expressed as algebraic expressions. This step-by-step solution involves using the Triangle Angle Sum Theorem and algebraic techniques, suitable for students in Grades 8-10.

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