https://r2.erweima.ai/mathbot/image/17248407871744uzy7xpx.jpg

m<URD = 2x, m<DRI = 3x + 14 and m<URI = 7x - 2 use the given figure to solve for x

Given the angles in the figure:

- \( m\angle URD = 2x \)
- \( m\angle DRI = 3x + 14^\circ \)
- \( m\angle URI = 7x - 2^\circ \)

Let's analyze the relationship between these angles:

### Step 1: Identify the Relationship
Angles \( \angle URD \), \( \angle DRI \), and \( \angle URI \) are all adjacent angles that share the common vertex \( R \) and lie along the line \( UD \). This implies that the sum of these three angles equals \( 180^\circ \) since they form a straight line.

### Step 2: Set Up the Equation
We can write the equation based on the angle sum property:
\[
m\angle URD + m\angle DRI + m\angle URI = 180^\circ
\]
Substituting the given expressions:
\[
2x + (3x + 14^\circ) + (7x - 2^\circ) = 180^\circ
\]

### Step 3: Simplify the Equation
Combine like terms:
\[
2x + 3x + 7x + 14^\circ - 2^\circ = 180^\circ
\]
\[
12x + 12^\circ = 180^\circ
\]

### Step 4: Solve for \( x \)
1. Subtract \( 12^\circ \) from both sides:
\[
12x = 168^\circ
\]

2. Divide both sides by 12:
\[
x = \frac{168^\circ}{12} = 14^\circ
\]

### Final Answer:
\[
x = 14^\circ
\]

Would you like a more detailed explanation or have any further questions?

### Relative Questions:
1. What is the angle sum property for angles on a straight line?
2. How do you solve for \( x \) when multiple angles are given in terms of \( x \)?
3. What is the relationship between adjacent angles on a straight line?
4. How do you verify if your solution for \( x \) is correct?
5. What would change if one of the angles was an exterior angle?

### Tip:
Always double-check your equation setup by verifying that all angles contribute correctly to the total angle sum, especially in problems involving straight lines or triangles.

Explore how to solve angle equations in a geometric figure with a detailed step-by-step solution. This problem involves identifying angle relationships and applying the angle sum property of a straight line. Suitable for high school 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