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\(\)In acute triangle \(ABC \),\( \angle A = 68^\circ.\) Let \(O\) be the circumcenter of triangle \(ABC\). Find\( \angle OBC\), in degrees.

 Feb 18, 2019

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 #1
avatar+21848 
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In acute triangle \(ABC,\ \angle A = 68^\circ\).

Let be the circumcenter of triangle \(ABC\).
Find, \(\angle OBC\) in degrees.

 

\(\text{Let $\angle OBC = {\color{red}x}$ } \)

\(\begin{array}{|rcll|} \hline 2{\color{red}x} + 2{\color{blue}y} + 2{\color{green}z} &=& 180^{\circ} \quad | \quad : 2 \\ {\color{red}x} + {\color{blue}y} + {\color{green}z} &=& 90^{\circ} \quad | \quad {\color{blue}y} + {\color{green}z} = \angle A \\ {\color{red}x} + A &=& 90^{\circ} \\ {\color{red}x} &=& 90^{\circ} - A \quad | \quad A = 68^{\circ} \\ {\color{red}x} &=& 90^{\circ} - 68^{\circ} \\ {\color{red}x} &=& 22^{\circ} \\ \hline \end{array}\)

 

\(\text{$\angle OBC$ in degrees is $22^{\circ}$}\)

 

laugh

 Feb 19, 2019
 #1
avatar+21848 
+4
Best Answer

In acute triangle \(ABC,\ \angle A = 68^\circ\).

Let be the circumcenter of triangle \(ABC\).
Find, \(\angle OBC\) in degrees.

 

\(\text{Let $\angle OBC = {\color{red}x}$ } \)

\(\begin{array}{|rcll|} \hline 2{\color{red}x} + 2{\color{blue}y} + 2{\color{green}z} &=& 180^{\circ} \quad | \quad : 2 \\ {\color{red}x} + {\color{blue}y} + {\color{green}z} &=& 90^{\circ} \quad | \quad {\color{blue}y} + {\color{green}z} = \angle A \\ {\color{red}x} + A &=& 90^{\circ} \\ {\color{red}x} &=& 90^{\circ} - A \quad | \quad A = 68^{\circ} \\ {\color{red}x} &=& 90^{\circ} - 68^{\circ} \\ {\color{red}x} &=& 22^{\circ} \\ \hline \end{array}\)

 

\(\text{$\angle OBC$ in degrees is $22^{\circ}$}\)

 

laugh

heureka Feb 19, 2019

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