Question
Download Solution PDFFor a regular polygon, the sum of the interior angles is 250% more than the sum of its exterior angles. Each interior angle of the polygon measures x°. What is the value of x?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The sum of all interior angle of polygon 250% more than the sum of exterior angles.
Formula used:
The sum of all interior angle of a polygon = (n - 2) × 180°
Where n = number of sides
Calculation:
According to question,
Sum if interior angles of polygon 250% more than the sum of exterior angles.
i.e. 350% of 360°
= 350% of 360°
= 3.5 × 360°
= 1260°
The sum of all interior angle of a polygon = (n - 2) × 180°
⇒ 1080° = (n - 2) × 180°
⇒ (1260°/180°) = (n - 2)
⇒ 7 = n - 2
⇒ n = 9
Now, each interior angle x = 1260°/9 = 140°
∴ The correct answer is option (1).
Last updated on Jul 21, 2025
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