Question

lesson 9.5 checkpoint

• complete the previous problems, check your solutions, then complete the lesson checkpoint below.
• complete the lesson reflection above by circling your current understanding of the learning goal(s).

find the value of x and y.

1. diagram: two intersecting lines forming vertical angles. angles labeled: ( 2(5x - 5)^circ ), ( (5y + 5)^circ ), ( (7y - 9)^circ ), ( (6x + 50)^circ )

Explanation:

Step1: Solve for x (Vertical Angles)

Vertical angles are equal, so \(2(5x - 5) = 6x + 50\).
Expand left side: \(10x - 10 = 6x + 50\).
Subtract \(6x\): \(4x - 10 = 50\).
Add 10: \(4x = 60\).
Divide by 4: \(x = 15\).

Step2: Solve for y (Vertical Angles)

Vertical angles are equal, so \(5y + 5 = 7y - 9\).
Subtract \(5y\): \(5 = 2y - 9\).
Add 9: \(14 = 2y\).
Divide by 2: \(y = 7\).

Answer:

\(x = 15\), \(y = 7\)