Two regular polygon are such that the ratio pf the measures their interior angles is 4 : 3 and the ratio
between their numbers od sides is 2:1. Find the number of sides of each polygon .
Answers
Answer:
ANSWER
Let number of sides of two polygons are n and 2n
measures of interior angles of x sided regular polygon is
x
(x−2)×180°
so
n
n−2
×180°
2n
2n−2
×180°
=
3
4
⇒
2(n−2)
2n−2
=
3
4
⇒6n−6=8n−16
⇒2n=10
⇒n=5
Therefore, number of sides of polygon are 5 and 10.
Step-by-step explanation:
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Solution(By Examveda Team)
In Give Question,
A + B = 8 ---- (i)
A + C =13 -----(ii)
B + D = 8 ----(iii)
C - D = 6 ----(iv)
Therefore equation (i) and (iii) are equal
A + B = B + D
=> A = D
Therefore, equation (iv) can be C - A = 6 ----- (v)
Now solving equation (ii) and (v), We Get C = 9.5 and A = 3.5
Put this value of A in equation in (i) B = 4.5 and value of C in equation (iv) we get D = 3.5
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Did u get that
A = 3.5
B = 4.5
C = 9.5
D = 3.5