https://file.aiquickdraw.com/mathbot/file/172720176712735evqedi.jpg

Let's go through the three problems presented in the image step by step:

---

### **Problem 13**
**If \( m\angle 1 = 78^\circ \), what is the \( m\angle 2 \) if the two angles are complementary?**

- **Complementary angles** sum up to \( 90^\circ \). Therefore, to find \( m\angle 2 \):
  \[
  m\angle 2 = 90^\circ - 78^\circ = 12^\circ
  \]
  
  **Answer for Problem 13: \( m\angle 2 = 12^\circ \)**

---

### **Problem 14**
**If \( \overline{BD} \) bisects \( \angle ABC \), solve for \( x \).**

- The given angle information:
  - \( \angle ABD = 30^\circ \)
  - \( \angle DBC = (x + 25)^\circ \)
- Since \( \overline{BD} \) bisects \( \angle ABC \), the two angles \( \angle ABD \) and \( \angle DBC \) must be equal:
  \[
  30^\circ = (x + 25)^\circ
  \]
  Solving for \( x \):
  \[
  x = 30^\circ - 25^\circ = 5^\circ
  \]

  **Answer for Problem 14: \( x = 5^\circ \)**

---

### **Problem 15**
**Solve for \( x \) and \( y \).**

- The given system involves two vertical angles, which are equal:
  - \( 5x = 12x - 41 \)
  - \( 5y = 5y \)
  
  From the first equation, solve for \( x \):
  \[
  5x = 12x - 41
  \]
  \[
  41 = 12x - 5x
  \]
  \[
  41 = 7x \quad \Rightarrow \quad x = \frac{41}{7} \approx 5.86
  \]
  
  For \( y \), since both equations involving \( y \) are the same, \( y \) is not uniquely determined by the problem, and the value for \( y \) remains arbitrary.

  **Answer for Problem 15: \( x \approx 5.86 \), \( y \) is arbitrary.**

---

Would you like more details on any of these steps?

Here are five related questions for further practice:
1. What are supplementary angles, and how do you calculate them?
2. How would you solve for a different variable in a bisected angle problem?
3. What happens when two angles are both complementary and bisected?
4. How can you check if a given system of linear equations has a unique solution?
5. How would you interpret a system of equations where one variable is not determined?

**Tip**: Always label your angle pairs and write out the equations based on their relationships (complementary, supplementary, bisected) for clarity!

If m∠1 = 78°, what is the m∠2 if the two angles are complementary? If BD bisects ∠ABC, solve for x. Solve for x and y given the equations in the figure.

Solve a set of angle-related problems, including complementary angles, bisected angles, and vertical angles. This guide provides step-by-step solutions 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