Three angles and a travelled distance
8 written marks
Three consecutive angles around a point are \(\theta\), \(\displaystyle 2\theta+\frac{\pi}{6}\) and \(\displaystyle 5\theta-\frac{\pi}{6}\). They fill one complete turn.
Part a · 3 marks
Find \(\theta\) and all three angles.
Part b · 2 marks
Identify the reflex angle and express it in degrees. Find the minor angle between the same two rays.
Part c · 3 marks
A point moves on a radius-\(12\) cm circle through the reflex angle and then through one additional complete turn, in the same direction. Find the exact total distance travelled.
Complete-answer checking, worked solutions and indicative written criteria.
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