https://file.aiquickdraw.com/mathbot/file/1728661851378hfzkgggl.jpg

We are given a triangle with three angles: \( 56^\circ \), \( (2x + 4)^\circ \), and \( x^\circ \). The sum of the angles in a triangle is always \( 180^\circ \). So, we can set up the equation as follows:

\[
56^\circ + (2x + 4)^\circ + x^\circ = 180^\circ
\]

Now, let's simplify and solve for \( x \):

1. Combine like terms:
   \[
   56 + 2x + 4 + x = 180
   \]
   \[
   60 + 3x = 180
   \]

2. Subtract 60 from both sides:
   \[
   3x = 120
   \]

3. Divide by 3:
   \[
   x = 40
   \]

Now that we have \( x = 40 \), we can find the measures of the three angles:

1. The first angle is given as \( 56^\circ \).
2. The second angle is \( (2x + 4)^\circ = 2(40) + 4 = 80 + 4 = 84^\circ \).
3. The third angle is \( x^\circ = 40^\circ \).

Thus, the three angles of the triangle are \( 56^\circ \), \( 84^\circ \), and \( 40^\circ \), which matches option **C**.

Would you like a more detailed explanation or have any questions?

---

Here are five related questions for further practice:
1. What is the sum of the interior angles of a polygon with 8 sides?
2. How would the equation change if the first angle was \( (3x + 2)^\circ \) instead of \( 56^\circ \)?
3. What are the properties of an equilateral triangle regarding its angles?
4. How do you find the missing angle in a right triangle if you are given two angles?
5. If one angle in a triangle is twice the size of another, how would you set up the equation to solve for the angles?

**Tip:** Always remember that the sum of the interior angles of a triangle is always \( 180^\circ \), regardless of the type of triangle.

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?

Learn how to solve for the unknown angles of a triangle when given one angle and algebraic expressions for the others. The solution involves the angle sum property of triangles and basic algebra. This problem is ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation