https://file.aiquickdraw.com/mathbot/file/1728122702369qaykl79w.jpg

The problem shows a triangle with two marked angles: \(58^\circ\) and another exterior angle labeled \(y^\circ\). The third angle of the triangle is opposite to the \(58^\circ\) angle, and since the triangle is isosceles (indicated by the two equal sides), this unmarked angle is also \(58^\circ\).

### Steps to Solve:
1. **Find the third angle inside the triangle**: 
   Since the sum of the interior angles in a triangle is \(180^\circ\), and two angles are \(58^\circ\) each, the third angle \( \theta \) can be calculated as:
   \[
   \theta = 180^\circ - 58^\circ - 58^\circ = 64^\circ
   \]

2. **Use the exterior angle theorem**:
   The exterior angle \(y^\circ\) is equal to the sum of the two opposite interior angles of the triangle. Here, the two opposite interior angles are both \(58^\circ\).
   \[
   y^\circ = 58^\circ + 58^\circ = 116^\circ
   \]

Thus, the value of \( y \) is \( \boxed{116^\circ} \).

Would you like more details or have any questions? 

Here are 5 related questions to explore:
1. What is the exterior angle theorem, and how does it apply to all triangles?
2. If the triangle were not isosceles, how would that affect the calculation of \(y\)?
3. Can the sum of exterior angles for any polygon be generalized like it is for triangles?
4. What happens if one angle inside the triangle is a right angle?
5. How do the properties of isosceles triangles apply to different geometric problems?

**Tip**: Always remember that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles!

Find the value of y in a triangle where one angle is 58°, the triangle is isosceles, and y is the exterior angle.

Learn how to find the value of y, the exterior angle of an isosceles triangle, using the Exterior Angle Theorem. This problem covers key concepts in geometry and is suitable 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