- 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

# Construct an angle of $ 45^{\circ} $ at the initial point of a given ray and justify the construction.

To do:

We have to construct an angle of $45^o$ at the initial point of a given ray and justify the construction.

Solution:

Steps of construction:

(a) Draw a ray $BC$.

(b) With center $B$ and a suitable radius draw an arc meeting $BC$ at $E$.

(c) With center $E$ and the same radius as above draw an arc intersecting the above arc at $F$

(d) With center $F$ and the same radius as above draw an arc intersecting the above arc at $G$

(e) With $E$ and $F$ as centers and radius more than $\frac{1}{2}EF$, draw two arcs meeting each other at $H$.

(f) Join $BH$ and produce it to $X$ so that $\angle XBC = 90^o$.

(g) Let $BH$ intersects the first arc at $D$

(h) With $D$ and $E$ as centers and radius greater than $\frac{1}{2}DE$, draw two arcs meeting each other at $K$

(i) Join $BK$ and extend it to $A$ forming ray $BA$

(j) Therefore, $\angle CBA=45^o$

Justification:

We have,

$\angle HBC=90^o$

We also have a perpendicular bisector $BA$ which divides $\angle HBC$

This implies,

$ABC=\frac{1}{2}HBC$

$ABC=\frac{1}{2}(90^o)$

$ABC=45^o$

Therefore, justified.

- Related Questions & Answers
- Find normal at a given point on the curve in C++
- Find Tangent at a given point on the curve in C++
- Java Program to Determine the Unicode Code Point at a given index
- Adding an element at a given position of the array in Javascript
- Explain the construction of finite and infinite language?
- Explain the construction and working of a Microwave Varactor diode.
- Get the arc sine of an angle in Java
- Get the arc cosine of an angle in Java
- Get the Trigonometric sin of an angle in Python
- Get the Trigonometric cosine of an angle in Python
- Get the Trigonometric tangent of an angle in Python
- Angle between a chord and a tangent when angle in the alternate segment is given in C++?
- Python Program to Construct an Expression Tree of a given Expression
- Python program to find angle between mid-point and base of a right angled triangle
- Explain the construction and working of a Microwave Schottky Barrier diode.
- How to set the angle of rotation of an Ellipse using FabricJS?