The sum of the interior angles of a regular polygon is 1260. Calculate the size of each exterior angle of the polygon.
Mathematics
ScanSolve AI Answer
Answer
The size of each exterior angle of the polygon is 40°.
Step-by-step solution
2 stepsSteps:
Find the number of sides (n) of the polygon.
The formula for the sum of the interior angles of a polygon is (n - 2) * 180°.
Given the sum is 1260°:
(n - 2) * 180° = 1260°
n - 2 = 1260 / 180
n - 2 = 7
n = 7 + 2
n = 9
The polygon has 9 sides (it's a nonagon).Calculate the size of each exterior angle.
For any regular polygon, the sum of its exterior angles is 360°. Since it's a regular polygon, all exterior angles are equal.
Each exterior angle = Sum of exterior angles / n
Each exterior angle = 360° / 9
Each exterior angle = 40°
Was this helpful?
Try one yourself
A new problem that tests the same skill.
Still stuck on this one?
Ask a follow-up, and the answer starts from this question.
Got a different question?Ask your own question
More Mathematics Questions
QA polygon has an interior angle sum of 1260^. Calculate the number of sides it has.QThe interior angles of a polygon are x°, 1/2x, (x+40)°, 110°, 135°, 160°. Find the value of x. 12…QDefine polygon, give examples. Find interior angle of regular hexagon. Find number of sides of…QThe sum of an interior angle and its corresponding exterior angle of any polygon is 180^.QIf the sum of interior angles of a regular polygon is 2340, 340. Find the number of side
Browse by topic:Geometry