The two corresponding angles formed by the intersection of two parallel lines by a transversal are (3x−20°) and (5 x−60°). Then, the value of (4x+30°) is :

Correct Answer: The correct option is 110 °.

Step-by-Step Explanation:

Step 1: Understand the geometric property
When two parallel lines are intersected by a transversal line, the corresponding angles formed are equal in measure.

Step 2: Set up the equation
Given the two corresponding angles as (3x - 20°) and (5x - 60°), we can set them equal to each other:
$3x-20=5x-60$

Step 3: Solve for x
Subtract 3x from both sides:
$-20=2x-60$

Add 60 to both sides:
$40=2x$

Divide by 2:
$x=20$

Step 4: Calculate the required value of (4x + 30°)
Substitute x = 20 into the expression (4x + 30°):
$4\left(20\right)+30=80+30=110\°$

Therefore, the value of (4x + 30°) is 110 °.