https://file.aiquickdraw.com/mathbot/file/1726613747713szaz7m4j.jpg

Let's go through the questions one by one based on the figures shown in the image.

### For Questions 11–14, use the figure on the left:

#### 11. Which point is the vertex of all the angles in this figure?
The vertex is where all the lines intersect, which is point **B**.

**Answer:** B. **B**

#### 12. What type of angle is ∠ABC?
∠ABC appears to be a right angle since the other figure states that ∠EBF = 50°, and we see that ∠ABC is formed by two perpendicular lines (horizontally along AB and vertically along BC).

**Answer:** B. **right angle**

#### 13. Which is true?
Looking at the figure, ∠EBF is given as 50°. So, the correct statement about ∠EBF is:
C. **m∠EBF = 50**

**Answer:** C. **m∠EBF = 50**

#### 14. For what value of x is ∠ATK ≅ ∠MJS if m∠ATK = 5x + 4 and m∠MJS = 8x − 11?
We set the angles equal since they are congruent:
\[
5x + 4 = 8x - 11
\]
Solving for \(x\):

\[
5x + 4 = 8x - 11
\]
\[
4 + 11 = 8x - 5x
\]
\[
15 = 3x
\]
\[
x = 5
\]

**Answer:** D. **5**

---

### For Questions 15–17, use the figure on the right:

#### 15. Which pair of angles are vertical angles?
Vertical angles are formed by the intersection of two lines and are opposite each other. Based on the diagram, ∠RSX and ∠XSW are vertical angles.

**Answer:** D. **∠RSX, ∠XSW**

#### 16. Which angle is supplementary to ∠USV?
Supplementary angles add up to 180°. ∠TSU is supplementary to ∠USV because they form a straight line.

**Answer:** A. **∠TSU**

#### 17. Find x and y.
From the diagram, we know:
- ∠USV = 5x°
- ∠TSU = 10y + 10°
Since ∠TSU and ∠USV are supplementary, we have:

\[
5x + (10y + 10) = 180
\]

Also, we know ∠RSX = 4x°, and since ∠RSX is vertically opposite to ∠TSU, we have:

\[
4x = 10y + 10
\]

Let's solve these two equations step by step. 

I'll calculate the values for \(x\) and \(y\):The solution is \(x = 20\) and \(y = 7\).

**Answer:** B. **x = 20, y = 7**

---

Do you need further details or explanations? Here are 5 related questions you might find helpful:

1. What are the properties of vertical angles?
2. How can we identify supplementary angles in a diagram?
3. Why do the measures of supplementary angles add up to 180°?
4. Can we use other methods to solve for \(x\) and \(y\) in this kind of problem?
5. How are congruent angles defined in geometry?

**Tip:** Always label known angles in diagrams to simplify angle-related problems.

For questions 11-17, refer to the figures and answer based on angle relationships, such as vertical, supplementary, and congruent angles. Solve for x and y in equations given for angle measures.

In this geometry problem, students will learn how to identify vertical and supplementary angles and solve for unknowns x and y using algebra. Explore key concepts such as congruent angles and the Vertical Angle Theorem. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation