Each interior angle of a regular polygon is 140°. What is the sum of the interior angles of a polygon with twice as many sides?

1,260°Correct answerYour answer2,520°Correct answerYour answer2,880°Correct answerYour answer3,240°Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Exterior angle = $180^\circ - 140^\circ = 40^\circ$ , so the polygon has $360 \div 40 = 9$ sides.
Twice as many sides = 18.
Angle sum = $(18 - 2) \times 180^\circ = 16 \times 180^\circ = 2{,}880^\circ$ .

Worth noting

Doubling the sides does not double the angle sum: $2 \times 1{,}260^\circ = 2{,}520^\circ$ is wrong because the '− 2' is not doubled. 3,240° forgets the '− 2' altogether.

Concept: Angle sum of a polygon from its number of sides
Typical timeTypical: 115 s
Your timeYours: —

The rule this testsQuadrilaterals and polygons

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Ten questions from Lines, Triangles and Circles, at your own pace.

Each interior angle of a regular polygon is 140°. What is the sum of the interior angles of a polygon with twice as many sides?

Explanation