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With only knowing the angles of $B$, $C$, and $D$ (shown above), is it possible to find the interior angle $A$? And if so, how?

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Yes. The interior angle is always double the inscribed angle (in your case $D$).

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  • $\begingroup$ So A would be 140°? $\endgroup$ – Jamie Sanborn May 28 '15 at 20:16
  • $\begingroup$ @JamieSanborn - yes. $\endgroup$ – nbubis May 28 '15 at 20:17

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