Question

geometry
1 - 7 hw #1 vertical angles
find the value of x.
1)
2)
3)
4)
5)
6)

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. For problem 1: \(74 = 8x+10\).

Step2: Solve the equation

Subtract 10 from both sides: \(74 - 10=8x\), so \(64 = 8x\). Divide both sides by 8: \(x=\frac{64}{8}=8\).

For problem 2: \(73=8x + 9\). Subtract 9 from both sides: \(73-9 = 8x\), so \(64=8x\). Divide by 8: \(x = 8\).

For problem 3: \(x + 36+2x=180\) (linear - pair angles sum to \(180^{\circ}\)). Combine like terms: \(3x+36 = 180\). Subtract 36: \(3x=180 - 36=144\). Divide by 3: \(x = 48\).

For problem 4: \(2x+27=3x\) (vertical angles). Subtract \(2x\) from both sides: \(x = 27\).

For problem 5: \(5x+4=4x + 12\) (vertical angles). Subtract \(4x\) from both sides: \(x+4=12\). Subtract 4: \(x = 8\).

For problem 6: \(9x-5+7x + 11=180\) (linear - pair angles sum to \(180^{\circ}\)). Combine like terms: \(16x+6 = 180\). Subtract 6: \(16x=174\). Divide by 16: \(x=\frac{174}{16}=\frac{87}{8}=10.875\).

Answer:

1. \(x = 8\)
2. \(x = 8\)
3. \(x = 48\)
4. \(x = 27\)
5. \(x = 8\)
6. \(x = 10.875\)