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The problem shows an isosceles triangle with one of the base angles marked as 56°. Since it is an isosceles triangle, the two base angles are equal. The other angle, labeled \( x^\circ \), is the vertex angle.

In any triangle, the sum of the interior angles is always 180°. Therefore, we can use the following equation to find the value of \( x \):

\[
x + 56 + 56 = 180
\]

Simplifying:

\[
x + 112 = 180
\]

\[
x = 180 - 112
\]

\[
x = 68^\circ
\]

So, the value of \( x \) is **68°**.

Would you like more details or explanations? Here are 5 related questions you might find useful:

1. How do you solve for the angles of a triangle if two angles are unknown?
2. What are the properties of an isosceles triangle?
3. How do you calculate the exterior angles of a triangle?
4. Can an isosceles triangle ever have a right angle?
5. What is the relationship between the angles and sides in different types of triangles?

**Tip:** Always remember that the sum of the angles in any triangle is 180°.

What is the value of x in an isosceles triangle where one of the base angles is 56°?

Learn how to find the vertex angle (x) in an isosceles triangle where one of the base angles is 56°. This problem involves understanding the sum of interior angles in a triangle and the properties of isosceles triangles. Suitable for students in Grades 7-10.

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