https://file.aiquickdraw.com/mathbot/file/1727942732092mdw8qp98.jpg

To find the value of \( x^\circ \) in this triangle, we can apply the **exterior angle theorem**.

### Exterior Angle Theorem:
In any triangle, the exterior angle is equal to the sum of the two opposite interior angles. The two given angles, 132° and 125°, are exterior angles. This theorem allows us to compute the missing interior angle \( x \).

The key step is recognizing that an exterior angle and the adjacent interior angle are supplementary (they add up to 180°). 

1. For the angle adjacent to 132°, the corresponding interior angle is:
   \[
   \text{Interior Angle} = 180^\circ - 132^\circ = 48^\circ
   \]

2. For the angle adjacent to 125°, the corresponding interior angle is:
   \[
   \text{Interior Angle} = 180^\circ - 125^\circ = 55^\circ
   \]

Now, we can find \( x^\circ \) by using the fact that the sum of the angles in any triangle is 180°:
\[
x^\circ = 180^\circ - (48^\circ + 55^\circ) = 180^\circ - 103^\circ = 77^\circ
\]

Thus, the value of \( x \) is:
\[
x = 77^\circ
\]

Would you like a detailed breakdown of these steps or have any questions?

Here are five related questions to explore:
1. What is the exterior angle theorem, and how does it apply to other polygons?
2. Can you solve for an unknown angle if only one exterior angle is given?
3. How would this approach change if the triangle were scalene or isosceles?
4. What happens if all angles in a triangle are given as exterior angles?
5. How do the properties of interior and exterior angles change for non-triangular shapes?

**Tip:** Always remember that the sum of the interior angles of any triangle is 180°, a fundamental property of triangles that simplifies many angle-related problems.

Find the value of x in a triangle where the two exterior angles are 132° and 125°.

Learn how to find the value of the interior angle x of a triangle where two exterior angles are given as 132° and 125°. This solution involves the use of the exterior angle theorem and the sum of interior angles property. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation