if the angles of Septagon are in the ratio 2 : 4 : 3 : 1 : 1 : 2, then calculate the measure of these angle
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Answer:
54°
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""" ❤️ Answer ❤️ """
Let the angles of the Pentagon be 2x,3x,4x,5x,and6x
Let n be the number of sides.
In a regular Pentagon, sum of interior angles
=
(n−2)×
180 ∘
= (5−2)×
180 ∘
540 ∘
According to the question,
2x+ 3x+ 4x+ 5x+ 6x=
540 ∘
⇒ 20x=
540 ∘
⇒ x=
20
540 ∘
=
27 ∘
The interior angles of the given pentagon
2x= 2×
27 ∘
54 ∘
3x= 3×
27 ∘
81 ∘
4x= 4×
27 ∘
108 ∘
5x= 5×
27 ∘
135 ∘
6x= 6×
27 ∘
162 ∘
thus, the interior angles of the Pentagon are
81
∘
108
∘
135
∘
54 ∘
and
162 ∘
Sum of first and second angle
=
54 ∘
81 ∘
135
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