- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
In the given figure, $A B C D$ is trapezium with $A B \| D C$. The bisectors of $\angle B$ and $\angle C$ meet at point $O$. Find $\angle B O C$."
Given: In the given figure, $A B C D$ is trapezium with $A B \| D C$. The bisectors of $\angle B$ and $\angle C$ meet at point $O$. Find $\angle B O C$.
To do: To find $\angle BOC$.
Solution:
In the given figure,
$\angle B+\angle C=180^o$
$\Rightarrow \frac{1}{2}\times \angle ABC+\frac{1}{2}\times \angle BCD=\frac{180}{2}=90^o$
$\Rightarrow \frac{\angle ABC}{2}+\frac{\angle BCD}{2}=90^o$
$\Rightarrow \angle OBC+\angle OCB=90^o$
In $\vartriangle BOC$,
$\angle OCB+\angle OBC+\angle BOC=180^o$
$\Rightarrow 90^o+\angle BOC=180^o$
$\Rightarrow \angle BOC=180^o-90^o$
$\Rightarrow \angle BOC=90^o$
Advertisements