What is the ratio of an interior angle of a pentagon and a hexagon?
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Let the angles of the Pentagon be 2x,3x,4x,5x, and 6x
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 54
∘
,81
∘
,108
∘
,135
∘
and 162
∘
Sum of first and second angle=54
∘
+81
∘
=135
∘
Hope it helps
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