दी गई आकृति में, $\angle OAB = 30^\circ$ और $\angle OCB = 57^\circ$, तो दर्शाइए कि $\angle BOC$ और $\angle AOC$ हैं। **Diagram Details:** 1. **Circle Diagram:** A circle with center $O$ has points $A$, $B$, and $C$ on its circumference. Radii $OA$, $OB$, and $OC$ are drawn, with tick marks showing $OA = OB = OC$. Chords $AB$ and $BC$ are also drawn forming triangles $\triangle OAB$ and $\triangle OBC$. A chord connecting $A$ and $C$ is drawn. The diagram indicates $\angle OAB = 30^\circ$, $\angle OBA = 30^\circ$, $\angle AOB = 120^\circ$, and in $\triangle OBC$, $\angle OCB = 57^\circ$, $\angle OBC = 57^\circ$, with $\angle BOC = 66^\circ$. 2. **Triangle $\triangle AOB$:** An isosceles triangle $AOB$ is shown separately with $OA = OB$. $\angle OAB = 30^\circ$, $\angle OBA = 30^\circ$, and the vertex angle $\angle AOB = 120^\circ$. $$\angle AOB + 30^\circ + 30^\circ = 180^\circ$$ $$\angle AOB = 120^\circ$$ In $\triangle BOC$: $$\angle BOC + 57^\circ + 57^\circ = 180^\circ$$ $$\angle BOC + 114^\circ = 180^\circ$$ $$\angle BOC = 180^\circ - 114^\circ$$ $$\angle BOC = 66^\circ$$

उत्तर: $$\angle BOC = 66^\circ \quad \text{तथा} \quad \angle AOC = 54^\circ$$

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