Question

angle 3 equals 5x - 2. angle 5 equals 2x + 7. what is the value of x? 25 degrees 175 degrees 123 degrees 57 degrees

Explanation:

Step1: Identify angle relationship

Since angle 3 and angle 5 are alternate - interior angles (assuming the two horizontal lines are parallel), they are equal. So we set up the equation $5x - 2=2x + 7$.

Step2: Solve the equation for x

Subtract $2x$ from both sides: $5x-2x - 2=2x-2x + 7$, which simplifies to $3x-2 = 7$.

Step3: Isolate the term with x

Add 2 to both sides: $3x-2 + 2=7 + 2$, getting $3x=9$.

Step4: Solve for x

Divide both sides by 3: $\frac{3x}{3}=\frac{9}{3}$, so $x = 3$.

Answer:

$x = 3$