The three angles of a triangle have measures of 56°
, (2x+4)°
 and x°
.

What are the measures of the three angles of the triangle?
A.56°
, 80°
, ​​​​44°

B.56°
, 90°
, 34°

C.56°
, 84°
, ​​​​40°

D.56°
, 60°
, ​​​​64°


To solve this problem, we use the fact that the sum of the angles in any triangle is always 180°. The three angles of the triangle are given as:

- 56°
- \( (2x + 4)° \)
- \( x° \)

### Step 1: Set up the equation for the sum of the angles:
\[
56° + (2x + 4)° + x° = 180°
\]

### Step 2: Combine like terms:
\[
56° + 2x° + 4° + x° = 180°
\]
\[
60° + 3x° = 180°
\]

### Step 3: Solve for \( x \):
\[
3x = 180° - 60°
\]
\[
3x = 120°
\]
\[
x = 40°
\]

### Step 4: Find the measures of the three angles:
- The first angle is 56°.
- The second angle is \( 2x + 4 = 2(40) + 4 = 80° \).
- The third angle is \( x = 40° \).

Thus, the three angles of the triangle are **56°**, **80°**, and **40°**.

### Conclusion:
The correct answer is:
**A. 56°, 80°, 44°**

Would you like more details on how we derived this, or do you have any questions?

Here are 5 related questions:
1. What is the sum of the angles of a triangle in a non-Euclidean geometry?
2. How would you solve for \(x\) if one angle was a right angle (90°)?
3. Can you form a triangle where one angle is greater than 90° and another is less than 45°?
4. How do the angles of a triangle change if one side lengthens while others remain constant?
5. How would the solution change if you were solving for a triangle in degrees and radians?

**Tip:** Always check the sum of the angles after solving any triangle-related problem to ensure accuracy!

The three angles of a triangle have measures of 56°, (2x+4)°, and x°. What are the measures of the three angles of the triangle? A. 56°, 80°, 44° B. 56°, 90°, 34° C. 56°, 84°, 40° D. 56°, 60°, 64°

Learn how to solve for the angles of a triangle where the angles are given as 56°, (2x + 4)°, and x°. This problem demonstrates how to apply the Triangle Angle Sum Theorem and solve linear equations to find the unknown angles. Suitable for students in Grades 6-8.

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