The Polygon Angle-Sum Theorems | Baamboozle - Baamboozle

If each interior angle of a regular polygon is 150°, how many sides does it have?

Interior angle = 150°, so exterior = 180 -150 = 30° → 360 ÷ 30 =12 360÷30= 12 sides

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A polygon has 8 sides. Find the sum of its interior angles and each interior angle if it is regular.

( 8 − 2 ) × 180 = 6 × 180 = 1080 ∘ (8−2)×180=6×180=1080 ∘ ; each angle = 1080 ÷ 8 = 135 ∘ 1080÷8= 135 ∘

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LOL YOU LOST 25 POINTS!!!

SIKE!!1 YOU WON 25 POINTS LOL!!

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What is the sum of the exterior angles of a 15-gon?

Always 360

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What type of polygon has an interior angle sum of 900°?

( 𝑛 − 2 ) × 180 = 900 (n−2)×180=900 → 𝑛 − 2 = 5 n−2=5 → 𝑛 = 7 n= 7 → Heptagon

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Find the measure of one exterior angle of a regular dodecagon (12 sides).

360 ÷ 12 = 30 ∘ 360÷12= 30 ∘

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A regular polygon has 18 sides. Find the measure of one interior angle.

(18−2)×180=2880; each angle = 2880 ÷ 18 = 160 ∘ 2880÷18= 160 ∘

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Find the measure of each interior angle of a regular hexagon.

( 6 − 2 ) × 180 = 720 ∘ each angle = 720 ÷ 6 = 120 ∘ 720÷6= 120 ∘

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A polygon has an interior angle sum of 1440°. How many sides does it have?

( 𝑛 − 2 ) × 180 = 1440 (n−2)×180=1440 → 𝑛 − 2 = 8 n−2=8 → 𝑛 = 10 n= 10

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A polygon has 6 more sides than a pentagon. What is the sum of its interior angles?

A pentagon has 5 sides → 5 + 6 = 11 sides Sum = ( 11 − 2 ) × 180 = 9 × 180 = 1620 ∘ (11−2)×180=9×180= 1620 ∘

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What is the sum of the interior angles of a 14-gon?

(14−2)×180=12×180= 2160 ∘

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A regular polygon has 24 sides. Find the measure of each interior angle.

(24−2)×180=3960 ∘ ; each interior angle = 3960 ÷ 24 = 165 ∘ 3960÷24= 165 ∘

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True or False: The sum of the exterior angles of any polygon is 180°.

False — it’s always 360°

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