Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
If the interior angles of a pentagon are in the ratio 1:2:3:4:5, find the measure of the smallest angle.
36°
40°
45°
30°
36°
Sum the ratio parts (1+2+3+4+5=15). Calculate total interior sum as (5-2)*180 = 540. Divide 540 by 15 to get the value of one unit (36). The smallest angle is 1 unit, which is 36.
A pentagon with interior angles in the ratio 1:2:3:4:5.
(n−2)×180°
Sum the ratio parts (1+2+3+4+5=15). Calculate total interior sum as (5-2)*180 = 540. Divide 540 by 15 to get the value of one unit (36). The smallest angle is 1 unit, which is 36.
Students often use the formula for a single interior angle of a regular polygon, (n−2)×180°/n, which is incorrect here because the pentagon is not regular.
Calculate sum of interior angles
For a polygon with n sides, the sum of interior angles is given by (n−2)×180°. For a pentagon, n=5.
(5−2)×180°=3×180°=540°
Set up equation using ratio
Let the angles be 1x,2x,3x,4x, and 5x. The sum of these angles must equal 540°.
1x+2x+3x+4x+5x=540°
Solve for x
Summing the coefficients: 15x=540°. Dividing by 15 gives the value of the smallest ratio part.
x=15540°=36°
A is correct because the smallest angle corresponds to 1 part of the ratio, which equals 36°.
This same logic applies to triangles, quadrilaterals, or any n-sided polygon; always check the value of n first to determine the total degrees.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants