Question

∠e and ∠f are vertical angles with m∠e = 5x + 10 and m∠f = 7x - 12. what is the value of x?
25
7
15
11
question 6
1 pts
∠e and ∠f are vertical angles with m∠e = 8x + 8 and m∠f = 2x + 38. what is the value of x?
5
17
8
3

Explanation:

Step1: Set the angle - measures equal

Since vertical angles are congruent, we set \(m\angle E=m\angle F\). For the first problem, \(5x + 10=7x-12\).

Step2: Isolate the \(x\) - terms

Subtract \(5x\) from both sides: \(5x + 10-5x=7x-12 - 5x\), which simplifies to \(10 = 2x-12\).

Step3: Solve for \(x\)

Add 12 to both sides: \(10 + 12=2x-12 + 12\), so \(22 = 2x\). Then divide both sides by 2: \(\frac{22}{2}=\frac{2x}{2}\), and \(x = 11\).

For the second problem:

Step1: Set the angle - measures equal

Set \(8x + 8=2x+38\) since \(m\angle E=m\angle F\) (vertical angles are equal).

Step2: Isolate the \(x\) - terms

Subtract \(2x\) from both sides: \(8x + 8-2x=2x+38 - 2x\), getting \(6x + 8=38\).

Step3: Solve for \(x\)

Subtract 8 from both sides: \(6x+8 - 8=38 - 8\), so \(6x = 30\). Divide both sides by 6: \(\frac{6x}{6}=\frac{30}{6}\), and \(x = 5\).

Answer:

For the first question: \(x = 11\)
For the second question: \(x = 5\)