Kuulchat - Senior High School (S.H.S) Mathematics Triangles & Polygons Practice Test Questions

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TRIANGLES & POLYGONS

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1.

In the diagram, JKLMN is a regular pentagon and KOPQRL is a regular hexagon. Find:

(a)

∠ JNM;

(b)

∠ KOP;

(c)

∠ MLR.

Show Solution

Each interior angle of a regular polygon = $\frac{(n-2) x 180°}{n}$

Where n = number of sides of the regular polygon.

(a)

Pentagon has 5 sides ⇒ n = 5

∠ JNM = $\frac{(5-2) x 180°}{5}$

∠ JNM = $\frac{3 x 180°}{5}$ = 108°

(b)

Hexagon has 6 sides ⇒ n = 6

∠ KOP = $\frac{(6-2) x 180°}{6}$

∠ KOP = $\frac{4 x 180°}{6}$ = 120°

(c)

∠ 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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