https://file.aiquickdraw.com/mathbot/file/17266715107906t2ksckz.jpg

**Directions - use the diagram to the find the following values:**



**y =**  

 **degrees**


**x =**  

 **degrees**


In the provided diagram, we have a triangle \( \triangle ABC \) with the angles at \( A \), \( B \), and \( C \) given. Let's solve for \( y \) and \( x \).

### Step 1: Calculate \( y \)
The sum of angles in a triangle is always 180°. The given angles are:
- \( \angle A = 73^\circ \)
- \( \angle B = 62^\circ \)

So, we can find \( y = \angle C \) by subtracting the sum of \( \angle A \) and \( \angle B \) from 180°:
\[
y = 180^\circ - 73^\circ - 62^\circ
\]
\[
y = 45^\circ
\]

### Step 2: Calculate \( x \)
The angle \( x \) is the exterior angle to \( \triangle ABC \) at point \( C \). By the exterior angle theorem, an exterior angle is equal to the sum of the two opposite interior angles of the triangle. Therefore:
\[
x = \angle A + \angle B
\]
\[
x = 73^\circ + 62^\circ = 135^\circ
\]

### Final Answers:
- \( y = 45^\circ \)
- \( x = 135^\circ \)

Would you like more details on the solution? Here are some related questions for further exploration:

1. How is the exterior angle theorem applied in other types of triangles?
2. What are the properties of an isosceles triangle, and how do they differ from a scalene triangle like this one?
3. Can we calculate the lengths of sides given only the angles of a triangle?
4. How would the calculations change if this triangle were part of a different geometric shape, such as a polygon?
5. How do angle bisectors affect the properties of the angles within a triangle?

**Tip:** When dealing with triangles, always remember that the sum of the interior angles is 180°, and the exterior angle is equal to the sum of the two non-adjacent interior angles.

Use the diagram to find the values of y and x.

Learn how to find the interior and exterior angles of a triangle using the Triangle Angle Sum Theorem and Exterior Angle Theorem. In this example, given angles at A (73°) and B (62°), we calculate y = 45° and x = 135°.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation