The sum of all interior angles of a regular polygon is 1080 ∘ . What is the measure of each of its interior angles ?

The polygon's interior angle total is equal to 1080. Let n be the number of sides, then ∴ ( 2 n − 4 ) × 90 ∘ = 1080 ∘ 2 n − 4 = 1080 ∘ 90 ∘ = 12 2 n = 12 + 4 = 166 ⇒ n = 16 2 = 8Each angle = 1080 8 = 135 ∘

Expert answers to "The sum of all interior angles of a..."

Kyra Huff

Answered question

2022-12-30

The sum of all interior angles of a regular polygon is

1080^{\circ}

. What is the measure of each of its interior angles ?

Answer & Explanation

Keely Franco

Beginner2022-12-31Added 11 answers

The polygon's interior angle total is equal to 1080. Let n be the number of sides, then

∴ (2 n - 4) \times 90^{\circ} = 1080^{\circ} 2 n - 4 = \frac{1080^{\circ}}{90^{\circ}} = 12 2 n = 12 + 4 = 166 \Rightarrow n = \frac{16}{2} = 8

Each angle

= \frac{1080}{8} = 135^{\circ}

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