Share The Polygon Angle-Sum Theorems
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What is the sum of the interior angles of a decagon (10 sides)?
(10−2)×180=8×180=1440 ∘
Find the measure of each interior angle of a regular hexagon.
( 6 − 2 ) × 180 = 720 ∘ each angle = 720 ÷ 6 = 120 ∘ 720÷6= 120 ∘
What is the sum of the exterior angles of a 15-gon?
Always 360
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
Find the measure of one exterior angle of a regular dodecagon (12 sides).
360 ÷ 12 = 30 ∘ 360÷12= 30 ∘
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
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 ∘
True or False: The sum of the exterior angles of any polygon is 180°.
False — it’s always 360°
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 ∘
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
A regular polygon has each exterior angle measuring 20°. How many sides does the polygon have?
360 ÷ 20 = 18 360÷20= 18 sides
What is the sum of the interior angles of a 14-gon?
(14−2)×180=12×180= 2160 ∘
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 ∘
One interior angle of a regular polygon is 162°. How many sides does the polygon have?
Exterior angle = 180 − 162 = 18 ∘ 180−162=18 ∘ ; 360 ÷ 18 = 20 360÷18= 20 sides
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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