\(\)In acute triangle \(ABC \),\( \angle A = 68^\circ.\) Let \(O\) be the circumcenter of triangle \(ABC\). Find\( \angle OBC\), in degrees.
+26367 In acute triangle \(ABC,\ \angle A = 68^\circ\).
Let be the circumcenter of triangle \(ABC\).
Find, \(\angle OBC\) in degrees.
\(\text{Let $\angle OBC = {\color{red}x}$ } \)
\(\begin{array}{|rcll|} \hline 2{\color{red}x} + 2{\color{blue}y} + 2{\color{green}z} &=& 180^{\circ} \quad | \quad : 2 \\ {\color{red}x} + {\color{blue}y} + {\color{green}z} &=& 90^{\circ} \quad | \quad {\color{blue}y} + {\color{green}z} = \angle A \\ {\color{red}x} + A &=& 90^{\circ} \\ {\color{red}x} &=& 90^{\circ} - A \quad | \quad A = 68^{\circ} \\ {\color{red}x} &=& 90^{\circ} - 68^{\circ} \\ {\color{red}x} &=& 22^{\circ} \\ \hline \end{array}\)
\(\text{$\angle OBC$ in degrees is $22^{\circ}$}\)
+26367 In acute triangle \(ABC,\ \angle A = 68^\circ\).
Let be the circumcenter of triangle \(ABC\).
Find, \(\angle OBC\) in degrees.
\(\text{Let $\angle OBC = {\color{red}x}$ } \)
\(\begin{array}{|rcll|} \hline 2{\color{red}x} + 2{\color{blue}y} + 2{\color{green}z} &=& 180^{\circ} \quad | \quad : 2 \\ {\color{red}x} + {\color{blue}y} + {\color{green}z} &=& 90^{\circ} \quad | \quad {\color{blue}y} + {\color{green}z} = \angle A \\ {\color{red}x} + A &=& 90^{\circ} \\ {\color{red}x} &=& 90^{\circ} - A \quad | \quad A = 68^{\circ} \\ {\color{red}x} &=& 90^{\circ} - 68^{\circ} \\ {\color{red}x} &=& 22^{\circ} \\ \hline \end{array}\)
\(\text{$\angle OBC$ in degrees is $22^{\circ}$}\)
