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.