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The problem shown in the image states:

**The measures of the exterior angles of a triangle are \( 2x^\circ, 6x^\circ, \) and \( 7x^\circ \). Find the measure of the smallest exterior angle.**

### Solution:

For any triangle, the sum of the exterior angles is always \( 360^\circ \).

Given the exterior angles \( 2x^\circ \), \( 6x^\circ \), and \( 7x^\circ \), we can set up the equation:
\[
2x + 6x + 7x = 360^\circ
\]
\[
15x = 360^\circ
\]
Now, solve for \( x \):
\[
x = \frac{360^\circ}{15} = 24^\circ
\]

Thus, the measures of the exterior angles are:
\[
2x = 2(24^\circ) = 48^\circ
\]
\[
6x = 6(24^\circ) = 144^\circ
\]
\[
7x = 7(24^\circ) = 168^\circ
\]

The smallest exterior angle is \( 48^\circ \).

Would you like further details or have any questions?

### Related questions:
1. How do the interior and exterior angles of a triangle relate to each other?
2. What is the sum of the interior angles of a triangle?
3. Can a triangle have an exterior angle greater than \( 180^\circ \)?
4. How do exterior angles of polygons change with the number of sides?
5. Why is the sum of exterior angles of any polygon always \( 360^\circ \)?

### Tip:
Remember that for any polygon, no matter the number of sides, the sum of the exterior angles will always equal \( 360^\circ \).

The measures of the exterior angles of a triangle are 2x°, 6x°, and 7x°. Find the measure of the smallest exterior angle.

This problem involves finding the smallest exterior angle of a triangle with angles 2x°, 6x°, and 7x°. Use the sum of exterior angles theorem to solve for x and determine the smallest angle. Suitable for students in Grade 7-9.

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