Given: A quadrilateral with angles 120∘,30 ∘, and two unknown angles, where x and 70 ∘ form one pair.

Let's solve the problem step by step.

### Given:
- A quadrilateral with angles \(120^\circ\), \(30^\circ\), and two unknown angles.
- One of the unknown angles is \(x\), and it pairs with \(70^\circ\).

### Solution:

1. **Identify the known angles:**
   - Known angles: \(120^\circ\) and \(30^\circ\).
   - The angles \(x\) and \(70^\circ\) are a pair, likely opposite each other in some contexts.

2. **Sum of angles in a quadrilateral:**
   - The sum of all interior angles in a quadrilateral is always \(360^\circ\).
   \[
   \text{Sum of angles} = 120^\circ + 30^\circ + x + 70^\circ
   \]

3. **Formulate the equation:**
   \[
   120^\circ + 30^\circ + x + 70^\circ = 360^\circ
   \]
   \[
   220^\circ + x = 360^\circ
   \]

4. **Solve for \(x\):**
   \[
   x = 360^\circ - 220^\circ
   \]
   \[
   x = 140^\circ
   \]

### Answer:
The value of \(x\) is \(140^\circ\).

---

Would you like to explore further or need additional explanations? Here are some related questions to consider:

1. How do you determine the sum of interior angles for polygons with more than four sides?
2. What are the steps to find missing angles when two angles are paired?
3. How does the relationship between opposite angles in a quadrilateral differ from adjacent angles?
4. Can you derive the sum of interior angles formula for a polygon with \(n\) sides?
5. What is the role of supplementary angles in finding unknowns in quadrilaterals?

**Tip:** When dealing with polygons, always double-check that the sum of all known angles matches what you expect for that shape, especially if the shape is irregular.

Learn how to solve a quadrilateral angles problem involving angles 120°, 30°, and two unknowns, x and 70°. Follow a step-by-step solution to find the value of x, understand the sum of angles in a quadrilateral, and explore angle relationships. Suitable for high school students studying geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation