Siti is laying floor tiles against a straight wall MN. At point O on the wall, two grout lines create rays OA and OB on the same side of MN, forming three angles. Siti measures that angle MOA is 3/2 times angle BON, and angle AOB is 5/6 of angle MOA. What is angle MOA?
Show Worked Solution
Worked Solution
Step 1: Let angle BON = k. Then angle MOA = (3/2)k. angle AOB = (5/6) × (3/2)k = 5k/4.
Step 2: Straight-line sum: (3k/2) + (5k/4) + k = 180
6k/4 + 5k/4 + 4k/4 = 180
15k/4 = 180
k = 48
Step 3: angle MOA = (3/2) × 48 = 72
Verify: 72 + 60 + 48 = 180 ✓
Correct answer: 72°
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