https://file.aiquickdraw.com/mathbot/file/17295587992548faz7dig.jpg

In this image, we see a triangle where two sides are marked as congruent (indicated by the hash marks), making this an **isosceles triangle**. 

The angles opposite these congruent sides are also congruent. One angle is labeled as \( 32^\circ \), and the other is labeled as \( x + 4 \). 

To find the value of \( x \), follow these steps:

1. Since the sum of the interior angles in any triangle is always \( 180^\circ \), we can write the equation:

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

2. Simplify the equation:

   \[
   32^\circ + 2(x + 4) = 180^\circ
   \]
   
   \[
   32^\circ + 2x + 8 = 180^\circ
   \]

3. Combine like terms:

   \[
   40^\circ + 2x = 180^\circ
   \]

4. Subtract 40 from both sides:

   \[
   2x = 140^\circ
   \]

5. Finally, divide by 2:

   \[
   x = 70^\circ
   \]

So, the value of \( x \) is **70 degrees**.

Would you like more details or have any questions?

Here are some related questions for further practice:

1. What is the sum of all interior angles in a quadrilateral?
2. How do you find the missing angle in a right triangle?
3. How does knowing that a triangle is isosceles help solve problems?
4. What are the properties of an equilateral triangle?
5. Can an isosceles triangle have a right angle?

**Tip:** Always remember that the sum of interior angles in any triangle is \( 180^\circ \), which is useful when solving problems involving triangles.

Find the value of x in the given isosceles triangle where one angle is 32° and the other two angles are (x + 4)° each.

Solve for x in an isosceles triangle where one angle is 32° and the other two angles are (x + 4)°. Learn how to use the angle sum property and the isosceles triangle theorem in this step-by-step explanation. Suitable for students in Grades 8-10.

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