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The sum of the measures of the angles in the triangle
is 180°. What is the measure of each angle? Write and
solve an equation. Which algebraic property did you use?

We are given a triangle where the three angles are:

1. \( x^\circ \)
2. \( (x + 10)^\circ \)
3. \( (2x - 10)^\circ \)

We know that the sum of the interior angles of any triangle is \( 180^\circ \). So, we can write an equation to represent this:

\[
x + (x + 10) + (2x - 10) = 180
\]

Now, let's solve the equation:

### Step 1: Combine like terms
\[
x + x + 10 + 2x - 10 = 180
\]
\[
4x = 180
\]

### Step 2: Solve for \( x \)
\[
x = \frac{180}{4} = 45
\]

### Step 3: Find the measures of each angle
1. The first angle is \( x = 45^\circ \).
2. The second angle is \( x + 10 = 45 + 10 = 55^\circ \).
3. The third angle is \( 2x - 10 = 2(45) - 10 = 90 - 10 = 80^\circ \).

So, the three angles of the triangle are \( 45^\circ \), \( 55^\circ \), and \( 80^\circ \).

### Algebraic Property Used:
The property used is the **Addition Property of Equality**, where you combine like terms on both sides of the equation to maintain equality.

Would you like further clarification on any steps?

---

Here are five related questions to expand your understanding:

1. How would the equation change if one of the angles was an exterior angle?
2. What would happen if the sum of the angles was more than 180°? Can that occur in any type of geometry?
3. How does this method work for solving angles in a quadrilateral, where the sum is 360°?
4. Could you solve for the angles if one of them was expressed as \( 3x \) instead of \( x \)?
5. How would this process change for an isosceles triangle?

**Tip:** In any triangle, always check if the sum of the calculated angles equals 180° to verify your solution.

The sum of the measures of the angles in the triangle is 180°. What is the measure of each angle? Write and solve an equation. Which algebraic property did you use?

Learn how to solve for the angles of a triangle with angle measures x, x+10, and 2x-10 degrees. This solution involves algebraic steps and uses the Triangle Angle Sum Theorem, making it ideal for students in Grades 8-10.

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