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Sagot :
Here we are given a geometrical shape with the following inner and an arc angle as follows:
[tex]The property to note here is from geometric properties of a circle.Property: The inner angle is always the mean of corresponding verticaly opposite arc angles.
We can express the above property in lieu to the geometry question at hand. We see that the two arc angles:
[tex]\text{Arc CD = 55 degrees , Arc BG = ?}[/tex]Ther inner vertically opposite angle are:
[tex]<\text{ DFC < }BFG\text{= 40 degrees }[/tex]The property can be expressed mathematically as follows:
[tex]<\text{ DFC = }\frac{1}{2}\cdot\text{ ( Arc CD + Arc BG )}[/tex]Next plug in the respective values of angles and evaluate for the arc angle BG as follows:
[tex]\begin{gathered} 40\text{ = }\frac{1}{2}\cdot\text{ ( 55 + Arc BG )} \\ 80\text{ = 55 + Arc BG } \\ \text{\textcolor{#FF7968}{Arc BG = 25 degrees}} \end{gathered}[/tex]Therefore the correct option is:
[tex]\textcolor{#FF7968}{25}\text{\textcolor{#FF7968}{ degrees}}[/tex]
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