A geometry problem by Rama Devi

Geometry Level 2

If the angles of a pentagon are in the ratio 1:3:6:7:10 , then the smallest angle is ?


The answer is 20.

Rama Devi by Rama Devi , 43, India

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4 solutions

Siddharth Singh
Apr 25, 2015

Sum of all the angles of the pentagon is 540.Therefore - x+3x+6x+7x+10x=540. x=20 and it is the smallest angle.

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Noel Lo
Apr 27, 2015

540/(1+3+6+7+10) = 540/27 = 20

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Since the ratio is 1 : 3 : 6 : 7 : 10 1:3:6:7:10 , the total is 1 + 3 + 6 + 7 = 27 1+3+6+7=27 . The sum of the interior angles of pentagon is 54 0 ∘ 540^\circ . So the smallest angle is

1 27 ( 540 ) = \dfrac{1}{27}(540)= 2 0 ∘ \boxed{20^\circ}

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Dipak Prajapati
Jul 5, 2015

In response of siddharth singh

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