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In the diagram, JKLMN is a regular pentagon and KOPQRL is a regular hexagon. Find:
(a)
∠ JNM;
(b)
∠ KOP;
(c)
∠ MLR.
Each interior angle of a regular polygon = (n-2) x 180° n
Where n = number of sides of the regular polygon.
Pentagon has 5 sides ⇒ n = 5
∠ JNM = (5-2) x 180° 5
∠ JNM = 3 x 180° 5 = 108°
Hexagon has 6 sides ⇒ n = 6
∠ KOP = (6-2) x 180° 6
∠ KOP = 4 x 180° 6 = 120°
∠ MLR + ∠ RLK + ∠ RLM = 360°
∠ RLK = ∠ KOP = 120°
∠ RLM = ∠ JNM = 108°
∠ MLR + 120° + 108° = 360°
∠ MLR + 228° = 360°
∠ MLR = 360° - 228°
∠ MLR = 132°
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