Discussion
Two parallel lines are intersected by a transversal and the two interior angles so formed on the same side of the transversal are \((2x + 15^{\circ})\) and \((3x - 20^{\circ})\). Then, the value of \((4x + 6^{\circ})\) is :
Answer: A
The value of \(4x + 6^{\circ}\) is 154°.
Interior angles on the same side of a transversal cutting two parallel lines are supplementary:
\[ \begin{aligned} (2x + 15) + (3x - 20) &= 180 \\ 5x - 5 &= 180 \Rightarrow x = 37 \\ 4x + 6 &= 148 + 6 = 154 \end{aligned} \]
148° is 4x without adding the 6. Taking the two angles as equal, as for alternate angles, gives x = 35 and 146°.
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