Geometry and TrigonometryVery hardAngles formed by parallel lines
Geometry and Trigonometry practice question
Two parallel lines are cut by a transversal. One of the eight angles measures 47°. Which of the following is NOT a possible measure of another one of the eight angles?
- A. 47°
- B. 133°
- C. 43°Correct
- D. 180° − 47°
Answer: C. 43°
With parallel lines and a transversal, every angle equals either 47° (corresponding/vertical/alternate) or its supplement 133°. 43° never appears — it's the complement, a tempting-but-wrong trap. Note D equals 133°.
Why the other answers are wrong
- A. 47°
- 47° does appear — the vertical, corresponding, and alternate angles to the given one all measure 47°.
- B. 133°
- 133° is possible: it's the supplement of 47°, and every angle in the figure is either 47° or 133°.
- D. 180° − 47°
- 180° − 47° is just 133°, the supplement, which does appear among the eight angles.
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