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All 75 Exam Topics Step-by-Step Lesson
Practice 15-Q Timed Drill
Step-by-Step Lesson • Step 1 of 6

ARCH-M1-13: Regular Polygon Exterior Angles (360°/n), 3-Figure Bearings, Clock Angles & 2D Vectors/Transformations

Full 15-Q Timed Drill
Step 1 of 6 • The Core Idea

ARCH-M1-13: Why the 135s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~135s (Blows 90s Clock)
Step 1: Recall the exterior angle theorem for any convex polygon.
The sum of the exterior angles of any convex polygon is 360∘360^\circ. For a regular nn-gon, each exterior angle equals 360∘n\frac{360^\circ}{n}.

**Step 2: Solve for nn.**
n=360∘24∘=302=15n = \frac{360^\circ}{24^\circ} = \frac{30}{2} = 15
The Fast ShortcutTarget: 35s (Saves 100s)
Line 1 (Exterior Angle Identity): n=360∘e=360∘24∘n = \frac{360^\circ}{e} = \frac{360^\circ}{24^\circ}.
**Line 2 (Cancel 1212):** 302=15\frac{30}{2} = 15 sides (15s).
Where Students Lose Time: In 21 past UAT-UK questions (9.33% of Mathematics 1), candidates lose 100s by at each vertex of a polygon track, the runner's bearing changes by the exterior turn angle 360/n, not the interior angle. Instead, apply M5 with Maths 1 skill M5.4.
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