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CBSE
Mathematics
Grade 10
Angle Sum Property of a Quadrilater...
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The angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8. Find the smallest angle of the quadrilateral.
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Hint: We will first discuss the fact that sum of angles of quadrilateral is 360∘. Then, we will just assume the angle and find all other angles using the ratio and sum them all up and equate to 360∘, we will have with us, the measures of the smallest angle.
Complete step-by-step answer:
We will use the fact that the sum of angles of a quadrilateral is 360∘.
Sum of angles of quadrilateral is 360∘ ………(1)
Now, we have the ratio of angles as 2 : 3 : 5 : 8.
Let the first angle be 2x, so then according to the ratio, the angles will be 2x,3x,5x,8x.
Now using (1), we will have:-
2x+3x+5x+8x=360∘
Simplifying the LHS, we will have:-
18x=360∘
Taking the 15 from multiplication in LHS to division in RHS, we will have:-
x=360∘18=40∘2=20∘
Hence, x=20∘.
So, the angles will be 40∘,60∘,100∘,160∘.
∴ The smallest angle of the quadrilateral = 40∘
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