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Interior angle of a
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27 Jan 2025, 23:35
27 Jan 2025, 23:35
Expert Reply
00:00
Question Stats:
50% (00:20) correct
50% (01:02) wrong based on 6 sessions
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\(
\begin{array}{ll}
\text { Quantity } \boldsymbol{A} & \text { Quantity } \boldsymbol{B} \\
\text { Interior angle of a } & \text { Interior angle of a } \\
\text { polygon of } 5 \text { sides } & \text { polygon of } 6 \text { sides }
\end{array}\)
\begin{array}{ll}
\text { Quantity } \boldsymbol{A} & \text { Quantity } \boldsymbol{B} \\
\text { Interior angle of a } & \text { Interior angle of a } \\
\text { polygon of } 5 \text { sides } & \text { polygon of } 6 \text { sides }
\end{array}\)
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Interior angle of a
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03 Mar 2025, 09:30
03 Mar 2025, 09:30
Expert Reply
We need to compare the interior angle of a polygon of 5 sides with interior angle of polygon with 6 sides.
Since nothing is said about the type of polygon i.e. regular or irregular, a unique comparison cannot be formed between their angles.
For example, if both the polygons are regular, the measure of each of the angles of the 5 sided and 6 sided polygon would be $\(\frac{(5-2) \times 180}{5}=108 \& \frac{(6-2) \times 180}{6}=120\)$ respectively, which results in higher value in
column B. But if we consider a different case in which the polygons are not regular, the measure of one of the angles of 5 sided polygon might go higher than that of the measure of the angle of 6 sided polygon.
(Sum of the angles of an $\(n\)$ - sided polygon is $\((n-2) \times 180\)$ and if the polygon has all angles equal, the measure of each angle is $\(\frac{Sum of all angles}{ Number of angles} =\frac{(n-2) \times 180}{n}\)$ )
Hence the answer is (D).
Since nothing is said about the type of polygon i.e. regular or irregular, a unique comparison cannot be formed between their angles.
For example, if both the polygons are regular, the measure of each of the angles of the 5 sided and 6 sided polygon would be $\(\frac{(5-2) \times 180}{5}=108 \& \frac{(6-2) \times 180}{6}=120\)$ respectively, which results in higher value in
column B. But if we consider a different case in which the polygons are not regular, the measure of one of the angles of 5 sided polygon might go higher than that of the measure of the angle of 6 sided polygon.
(Sum of the angles of an $\(n\)$ - sided polygon is $\((n-2) \times 180\)$ and if the polygon has all angles equal, the measure of each angle is $\(\frac{Sum of all angles}{ Number of angles} =\frac{(n-2) \times 180}{n}\)$ )
Hence the answer is (D).
gmatclubot
Interior angle of a [#permalink]
03 Mar 2025, 09:30
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