Question
Download Solution PDFFor a regular polygon, the sum of the interior angles is 200% 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 200% 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
= 300% of 360°
= 3 × 360°
= 1080°
The sum of all interior angle of a polygon = (n - 2) × 180°
⇒ 1080° = (n - 2) × 180°
⇒ (1080°/180°) = (n - 2)
⇒ 6 = n - 2
⇒ n = 8
Now, each interior angle x = 1080°/8 = 135°
∴ The Required measure of x is 135°.
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