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Question Number 211323 by mr W last updated on 06/Sep/24

Commented by mr W last updated on 06/Sep/24

both circles are concentric.  find ∠C=?

$${both}\:{circles}\:{are}\:{concentric}. \\ $$$${find}\:\angle{C}=? \\ $$

Answered by liuxinnan last updated on 06/Sep/24

(1/2)∠DCA=∠OCA=∠OAC=(1/2)∠DAC=(o/2)  ∠B=π−∠BAC−∠DCA=π−3o

$$\frac{\mathrm{1}}{\mathrm{2}}\angle{DCA}=\angle{OCA}=\angle{OAC}=\frac{\mathrm{1}}{\mathrm{2}}\angle{DAC}=\frac{{o}}{\mathrm{2}} \\ $$$$\angle{B}=\pi−\angle{BAC}−\angle{DCA}=\pi−\mathrm{3}{o} \\ $$

Commented by liuxinnan last updated on 06/Sep/24

Commented by mr W last updated on 06/Sep/24

in the figure “o” is just a symbol  indicating that the two red angles   are equal. “o” is not a given value.

$${in}\:{the}\:{figure}\:``{o}''\:{is}\:{just}\:{a}\:{symbol} \\ $$$${indicating}\:{that}\:{the}\:{two}\:{red}\:{angles}\: \\ $$$${are}\:{equal}.\:``{o}''\:{is}\:{not}\:{a}\:{given}\:{value}. \\ $$

Commented by liuxinnan last updated on 06/Sep/24

Commented by mr W last updated on 06/Sep/24

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Answered by mr W last updated on 06/Sep/24

Commented by mr W last updated on 06/Sep/24

10α=180° ⇒α=18°  ⇒∠C=36°, ∠B=72°

$$\mathrm{10}\alpha=\mathrm{180}°\:\Rightarrow\alpha=\mathrm{18}° \\ $$$$\Rightarrow\angle{C}=\mathrm{36}°,\:\angle{B}=\mathrm{72}° \\ $$

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