##### How can I understand geometry in order to calculate the length of a circle?

label Mathematics
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Oct 30th, 2015

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The total angle of a circle is $\dpi{120} 360^{\circ}$.

So adding all the angles subtended by the arcs at the center should equal $\dpi{120} 360^{\circ}$.

Therefore,

$\\ 4x + 3x + 3x + 10^{\circ} + 2x + 2x - 14^{\circ} = 360^{\circ}\\ \\ 14x-4^{\circ}=360^{\circ}\\ \\ 14x=360^{\circ}+4^{\circ}\\ \\ 14x=364^{\circ}\\ \\ x=\frac{364}{14}\\ \\ x=26^{\circ}$

Hence,

$m\widehat{GU}=(3\times26+10)^{\circ}=88^{\circ}$

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Oct 30th, 2015

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Oct 30th, 2015
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Oct 30th, 2015
Sep 23rd, 2017
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