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Find the measure of the central angle indicated. Assume that lines which appear to be diameters are actual diameters.

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asked Oct 15, 2024 102k views

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Find the measure of the central angle indicated. Assume that lines which appear to be diameters are actual diameters.

Find the measure of the central angle indicated. Assume that lines which appear to-example-1

Mathematics
high-school

Louis Saglio asked

by Louis Saglio

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$\stackrel{\widehat{FI}}{85}~~ + ~~\stackrel{\widehat{IH}}{(50+x)}~~ + ~~\stackrel{\widehat{HG}}{(-9x-10)}~~ + ~~\stackrel{\widehat{GF}}{(-15x+5)}~~ = ~~360 \\\\\\ 130-23x=360\implies 130=360+23x\implies -230=23x\implies \cfrac{-230}{23}=x \\\\\\ -10=x\hspace{9em}\stackrel{\widehat{GF}}{-15(-10)+5}\implies \text{\LARGE 155}^o$