- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- 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 Fig. 6.16, if $ x+y=w+z $, then prove that $ \mathrm{AOB} $ is a line.

"

**To do:**

We have to prove that $AOB$ is a line.

**Solution:**

We know that,

The sum of the measures of the angles in linear pairs is always $180^o$.

So in order to prove that $AOB$ is a straight line, we have to prove that $x+y$ is a linear pair of $AOB$.

This implies,

$x+y=180^o$

We also know that,

The angles around a point give $360^o$.

This implies,

$x+y+w+z=360^o$

Since we have,

$x+y=w+z$

We get,

$2x+y=360^o$

This implies,

$x+y=\frac{360^o}{2}$

$x+y=180^o$

Therefore, $x+y$ is the linear pair

This implies, that $AOB$ is a line.

- Related Questions & Answers
- Prove that the Hamiltonian Path is NP-Complete in TOC
- Prove that the vertex cover is NP complete in TOC
- Prove that the interface for a primitive type is an empty array in Java
- Prove that the Cartesian product of a finite number of countable sets is countable?
- What is Wireless Fidelity 6 (WiFi 6)?
- Java if-then-else statement
- If-then-else in Lua Programming
- Performing mathematical operations in MySQL IF then ELSE is possible?
- Can you show some pictures that prove you a skilled photographer?
- Check If It Is a Straight Line in C++
- Prove that CFL is closed under union and star but not under intersection?
- Prove that Linear bounded automata LBA ⊂ PSPACE in TOC?
- What is if/then directives for debug vs release in C#?
- How to prove that only one instance of the object is created for static class?
- What is the resemblance of COALESCE() function with IF-THEN-ELSE statement?
- Prove that the polynomial time reduction is from the Clique problem to the Vertex Cover problem

Advertisements