Question

03 - hw finding angle pairs algebraically

1. solve for x:

100°
8x + 10

1. solve for x:

5x 2x + 24

1. solve for x:

3x + 25 6x - 5

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. For problem 1: \(8x + 10=100\)

Step2: Solve the equation

Subtract 10 from both sides: \(8x=100 - 10\), so \(8x = 90\). Then \(x=\frac{90}{8}=\frac{45}{4}=11.25\)

For problem 2: \(5x=2x + 24\)
Subtract \(2x\) from both sides: \(5x-2x=24\), so \(3x = 24\), then \(x = 8\)

For problem 3: \(3x + 25=6x-5\)
Subtract \(3x\) from both sides: \(25=6x - 5-3x\), so \(25 + 5=3x\), \(30=3x\), then \(x = 10\)

Answer:

1. \(x = 11.25\)
2. \(x = 8\)
3. \(x = 10\)