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Earlier discussion
5 older comments kept for context.
Victor Titus
The number of sides in a regular polygon can be determined from its interior angle using the formula:
\[\text{Interior Angle} = \frac{(n-2) \times 180}{n}\]
where \(n\) is the number of sides. In this case, the polygon has \(2k + 1\) sides and each interior angle measures 140 degrees. We can set up the equation:
\[140 = \frac{(2k + 1 - 2) \times 180}{2k + 1}\]
Solving this equation for \(k\) gives:
\[k = 4\]
So, if a regular polygon of \(2k + 1\) sides has 140 degrees as the size of each interior angle, then \(k = 4\).
The correct answer should be \(k = 4\).
Benjamin
The options are not correct, the original one I have has option A as 4
Albert Prince
which questions are you using bro ? I also have same
Ayomide Titiola
180-140=40
360/40=9
2k+1=9
2k=9-1,2k=8
k=8/2=4
Abdul-Lateef Olaoluwa
K is meant to be 4 actually.
The sum of each interior angles in a polygon is
[180(n - 2)] / n.
Since the sum of interior angles in the question equals 140. Therefore, [180(n - 2)] / n = 140.
Take 2k + 1 to be n. That is 2k + 1 = n
Do the math and make n the subject of the formula in [180(n - 2)] / n = 140. You get 9.
Remember 2k + 1 = n, Now we know n is 9. Substitute and you get 2k + 1 = 9.
Do the math and k is equal to 4.
We are asked to look for k and not the number of sides of the polygon.