Problem 3 · Use a full-turn invariant · 3 points
Made by AI and not reviewed by a real person.
Maya walks once around a triangular park, turning left at each corner to follow its sides. Her first turn is 30° larger than her second, and her third turn is 140°; how large is her second turn?
- 5°
- 125°
- 95°
- 110°
- 80°
Show a hint
- After a full lap, which way is Maya facing compared with when she started? Think about her total change in direction.
- The three turns make one full revolution. Find the total of the first two, then use the 30° difference.
Show the answer and solution
Answer: C — 95°
Maya makes one full turn, or 360°, during the lap. Her first two turns therefore add to 360° − 140° = 220°. Since the first is 30° larger, the second is (220° − 30°) ÷ 2 = 95°. The tempting 110° splits 220° equally but ignores the 30° difference.