The ratio of the exterior angle to the interior angle of ...
The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?
30
24
18
12
Correct answer is B
Let a represent an interior angle; e represent an exterior angle. A section of the polygon is down in the diagram.
\(\frac{e}{a}\) = \(\frac{l}{11}\) given
a = 11e
a + e = 180o(angles on a straight line)
11e + e = 180o
12e = 180o
e = \(\frac{180^o}{12}\)
= 15o
Hence, number of sides
= \(\frac{360^o}{\tect{size of one exterior angle}\)
= \(\frac{360^o}{14^o}\)
= 24
Similar Questions
Given a regular hexagon, calculate each interior angle of the hexagon...
Find the equation whose roots are -8 and 5...
If y = 23\(_{five}\) + 101\(_{three}\) , find y, leaving your answer in base two...
Each interior angle of a regular nonagon(nine sided polygon) is equal to...
Solve the inequality: \(\frac{2x - 5}{2} < (2 - x)\)...
If (0.25)\(^y\) = 32, find the value of y....
If log\(_{10}\)2 = 0.3010 and log\(_{10}\)7 = 0.8451, evaluate log\(_{10}\)280 ...
Which of the following could be the inequality illustrated in the sketch graph above? ...
Solve for x, If \(\frac{\frac{2}{x}}{\frac{1}{p^2} + \frac{1}{p^2}}\) = m...