Question

1. solve for x. (10x + 1)° (12x - 5)° 21. solve for x. (4x + 7)° (2x + 5)°

Explanation:

Step1: Identify vertical - angles property

Vertical angles are equal. So, \(12x - 5=10x + 1\).

Step2: Isolate the variable \(x\) terms

Subtract \(10x\) from both sides: \(12x-10x - 5=10x-10x + 1\), which simplifies to \(2x-5 = 1\).

Step3: Solve for \(x\)

Add 5 to both sides: \(2x-5 + 5=1+5\), so \(2x=6\). Then divide both sides by 2: \(x = 3\).

for second problem:

Step1: Identify vertical - angles property

Since vertical angles are equal, \(4x + 7=2x+5\).

Step2: Isolate the variable \(x\) terms

Subtract \(2x\) from both sides: \(4x-2x + 7=2x-2x+5\), which gives \(2x + 7=5\).

Step3: Solve for \(x\)

Subtract 7 from both sides: \(2x+7 - 7=5 - 7\), so \(2x=-2\). Divide both sides by 2: \(x=-1\).

Answer:

\(x = 3\)