https://file.aiquickdraw.com/mathbot/file/1725322672796ooiwof1c.jpg

Let's analyze the diagram provided to find the value of \( x^\circ \).

### Given:
- One angle is \( 28^\circ \) (at the bottom left).
- Another angle is \( 70^\circ \) (at the top right).
- There's a third angle \( x^\circ \) that we need to determine.

### Step-by-Step Solution:

1. **Identify the Quadrilateral:**
   - The figure appears to be a quadrilateral, with one angle \( 28^\circ \), another \( 70^\circ \), and two other angles (one of which is \( x \)).

2. **Sum of Angles in a Quadrilateral:**
   - The sum of the interior angles of any quadrilateral is always \( 360^\circ \).

3. **Determine the Remaining Angles:**
   - Since one of the angles is \( 90^\circ \) (as indicated by the right angle), we can now use the sum of angles to find \( x \).

   \[
   \text{Sum of angles} = 360^\circ
   \]

   So, the equation is:
   \[
   28^\circ + 90^\circ + 70^\circ + x = 360^\circ
   \]
   
4. **Solve for \( x \):**
   \[
   188^\circ + x = 360^\circ
   \]
   \[
   x = 360^\circ - 188^\circ
   \]
   \[
   x = 172^\circ
   \]

### Final Answer:
\[
x = 172^\circ
\]

Would you like a more detailed explanation, or do you have any other questions? Here are some related questions for further practice:

1. How do you determine the sum of angles in a polygon with \(n\) sides?
2. What are the properties of quadrilaterals in geometry?
3. How does the exterior angle theorem relate to quadrilaterals?
4. Can you prove why the sum of the interior angles of a quadrilateral is always \(360^\circ\)?
5. How would you approach finding unknown angles in irregular polygons?

**Tip:** When dealing with quadrilaterals, always remember that the sum of all interior angles is \(360^\circ\). This can help you solve for unknown angles when given the others.

Learn how to find the unknown angle x in a quadrilateral with given angles: 28°, 70°, and an additional angle x°. Follow a step-by-step solution using the sum of angles in a quadrilateral theorem. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation