Two parallel lines are intersected by a transversal and the two interior…
2024
Two parallel lines are intersected by a transversal and the two interior angles so formed on the same side of the transversal are (2x + 15°) and (3x - 20°). Then, the value of (4x + 6°) is:
- A.
154°
- B.
150°
- C.
148°
- D.
146°
Show answer & explanation
Correct answer: A
Concept: When two parallel lines are cut by a transversal, the interior angles that lie on the same side of the transversal (co-interior / consecutive interior angles) are supplementary — their measures always add up to 180°.
Let the two co-interior angles be (2x + 15)° and (3x − 20)°.
Since they lie on the same side of the transversal between the parallel lines, they are supplementary: (2x + 15) + (3x − 20) = 180.
Combine like terms: 5x − 5 = 180.
Solve for x: 5x = 185, so x = 37.
Substitute x = 37 into the required expression: 4x + 6 = 4(37) + 6 = 148 + 6 = 154°.
Cross-check: verify by checking the original angles at x = 37: 2(37) + 15 = 89° and 3(37) − 20 = 91°; their sum is 89° + 91° = 180°, confirming the supplementary relationship holds.
Hence, the value of (4x + 6°) is 154°.