Apedia Logo Apedia
Join

Choose Language

Select your preferred reading language
🇬🇧
English
✔
🇮🇳
हिन्दी
✔
✕
Full View
Geometry
Polygons
EN हिंदी
✕
RRB NTPC Graduate Tier 1 2025 Shift-1 📅 09 Jun, 2025

For 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?

A
140
B
150
C
145
D
120
Result Summary
Logo

APEDIA

RRB NTPC Graduate Tier 1
2025 • 09 Jun, 2025 • Shift-1
For 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?
Correct Answer
140
Foundational Geometric Properties: For absolutely any convex polygon, the sum of all external angles strictly equals 360°.Equation Formulation: The problem ......
Ref/Book : RRB NTPC Graduate Tier 1 2025
Ref. Subject Geometry
Chapter -
Ref. Topic Polygons
Pg. No -
💡 Analysis & Explanation
Foundational Geometric Properties ▼
For absolutely any convex polygon, the sum of all external angles strictly equals 360°.
Equation Formulation ▼
The problem states the internal sum is 250% MORE than the external sum. This means the Internal Sum = 360 + (2.5 * 360) = 360 + 900 = 1260°.
Determining the Number of Sides (n) ▼
The universal formula for the sum of interior angles is (n - 2) * 180. Setting this equal to our calculated sum gives: (n - 2) * 180 = 1260. Dividing both sides by 180 yields (n - 2) = 7. Thus, n = 9, representing a nonagon.
Final Angle Calculation ▼
Since it is a regular polygon with 9 equal sides, each interior angle x is calculated by dividing the total internal sum by the number of sides: 1260 / 9 = 140.
Conclusion ▼
The exact value of each interior angle x is 140.
← Prev
55 / 100
Next →