Discussion
Two alternate interior angles formed by the intersection of two parallel lines by a transversal are (5y - 10°) and (7y - 90°). Then, the value of (3y - 20°) is :
Answer: D
The value of \(3y - 20\) is 100°.
Alternate interior angles formed by a transversal across parallel lines are equal, so set the two expressions equal:
\[ \begin{aligned} 5y - 10 &= 7y - 90 \\ 2y &= 80 \Rightarrow y = 40 \\ 3y - 20 &= 120 - 20 = 100 \end{aligned} \]
The question tests only that equality. Note that with \(y = 40\) each given angle works out to \(190^{\circ}\), which a real interior angle cannot be, so the numbers do not describe an actual figure; the keyed answer is what the equality gives. 120° is \(3y\) without subtracting 20.
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