https://file.aiquickdraw.com/mathbot/file/1727356292193lf42q7ws.jpg

The question in the image is about an isosceles triangle and it reads:

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**In an isosceles triangle, the vertex angle is thrice the either of the base angles. Find the measure of each angle. On the basis of angles, classify the type of triangle it is.**

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Let’s break this down and solve it step by step.

### Solution:

1. **Given:**
   - Let the base angles of the isosceles triangle be \(x\).
   - The vertex angle is given to be three times the base angles, so the vertex angle is \(3x\).

2. **Sum of angles in a triangle:**
   The sum of angles in any triangle is always \(180^\circ\).

   So, for this triangle:
   \[
   x + x + 3x = 180^\circ
   \]
   Simplifying:
   \[
   5x = 180^\circ
   \]
   \[
   x = \frac{180^\circ}{5} = 36^\circ
   \]

3. **Finding the vertex angle:**
   Since the vertex angle is \(3x\):
   \[
   3x = 3 \times 36^\circ = 108^\circ
   \]

4. **Conclusion:**
   - The two base angles are \(36^\circ\) each.
   - The vertex angle is \(108^\circ\).

   The triangle has one angle greater than \(90^\circ\), which makes it an **obtuse triangle**.

### Final Answer:
- Base angles: \(36^\circ\)
- Vertex angle: \(108^\circ\)
- The triangle is an **obtuse isosceles triangle**.

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Do you have any questions or would you like a deeper explanation? Here are some related questions to explore:

1. What is the general property of angles in an isosceles triangle?
2. How do you classify triangles based on angles?
3. Why does the sum of the angles in a triangle always equal \(180^\circ\)?
4. How would the solution change if the vertex angle was twice the base angles?
5. Can you have an equilateral triangle where the vertex angle is different?

**Tip:** Always remember that the sum of the angles in any triangle is \(180^\circ\), which can be a handy check for your calculations.

In an isosceles triangle, the vertex angle is thrice the either of the base angles. Find the measure of each angle. On the basis of angles, classify the type of triangle it is.

Learn how to solve a problem involving an isosceles triangle where the vertex angle is three times the base angles. This solution covers the sum of angles in a triangle and explains how to classify the triangle based on the angles. Suitable for students in Grades 7-9.

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