Question

find the value of x for which a || b. a) 140 b) 35 c) 47 d) 145

Explanation:

Step1: Identify Angle Relationship

When lines \(a\) and \(b\) are parallel, the angles \(x^\circ\) and \((3x + 40)^\circ\) are same - side interior angles, and same - side interior angles are supplementary. So, we can write the equation \(x+(3x + 40)=180\).

Step2: Solve the Equation

First, combine like terms: \(x+3x+40 = 180\) simplifies to \(4x+40=180\).
Then, subtract 40 from both sides: \(4x=180 - 40\), so \(4x = 140\).
Finally, divide both sides by 4: \(x=\frac{140}{4}=35\).

Answer:

B) 35