- Trending Categories
- 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, $ O C $ and $ O D $ are the angle bisectors of $ \angle B C D $ and $ \angle A D C $ respectively. If $ \angle A=105^{\circ} $, find $ \angle B $.
"
Given: In the given figure, $OC$ and $OD$ are the angle bisectors of $\angle BCD$ and $\angle ADC$ respectively and $\angle A=105^{\circ}$.
To do: To find $\angle B$.
Solution:
$\because OD$ is the bisector of $ADC$
$\therefore OC$ is the bisector of $BCD$
$\Rightarrow \angle ADC=\angle D=\angle ODC\times 2$
$\Rightarrow \angle D=25^o\times 2=50^o$
Similarly: $\angle BCD=\angle C=OCD\times 2$
$\Rightarrow \angle C=30^o\times 2=60^o$
It is known that $A+B+C+D=360^o$ $( sum\ of\ angles\ of\ quadrilateral=360^o )$
$\Rightarrow 105^o+B+60^o+50^o=360^o$
$\Rightarrow 105^o+B+110^o=360^o$
$\Rightarrow B+105^o+110^o=360^o$
$\Rightarrow B+215^o=360^o$
$\Rightarrow B=360^o - 215^o$
$\Rightarrow B=145^o$
Thus, $\angle B=145^o$.