# Points, lines and angles  (Page 2/3)

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Angles are measured in degrees which is denoted by ${}^{\circ }$ , a small circle raised above the text in the same fashion as an exponent (or a superscript).

Angles can also be measured in radians. At high school level you will only use degrees, but if you decide to take maths at university you will learn about radians. Angle labelled as B ^ , ∠ C B A or ∠ A B C Examples of angles. A ^ = E ^ , even though the lines making up the angles are of different lengths.

## Measuring angles

The size of an angle does not depend on the length of the lines that are joined to make up the angle, but depends only on how both the lines are placed as can be seen in [link] . This means that the idea of length cannot be used to measure angles. An angle is a rotation around the vertex.

## Using a protractor

A protractor is a simple tool that is used to measure angles. A picture of a protractor is shown in [link] .

Method:

Using a protractor

1. Place the bottom line of the protractor along one line of the angle so that the other line of the angle points at the degree markings.
2. Move the protractor along the line so that the centre point on the protractor is at the vertex of the two lines that make up the angle.
3. Follow the second line until it meets the marking on the protractor and read off the angle. Make sure you start measuring at 0 ${}^{\circ }$ .

## Special angles

What is the smallest angle that can be drawn? The figure below shows two lines ( $CA$ and $AB$ ) making an angle at a common vertex $A$ . If line $CA$ is rotated around the common vertex $A$ , down towards line $AB$ , then the smallest angle that can be drawn occurs when the two lines are pointing in the same direction. This gives an angle of 0 ${}^{\circ }$ . This is shown in [link]

If line $CA$ is now swung upwards, any other angle can be obtained. If line $CA$ and line $AB$ point in opposite directions (the third case in [link] ) then this forms an angle of 180 ${}^{\circ }$ .

If three points $A$ , $B$ and $C$ lie on a straight line, then the angle between them is 180 ${}^{\circ }$ . Conversely, if the angle between three points is 180 ${}^{\circ }$ , then the points lie on a straight line.

An angle of 90 ${}^{\circ }$ is called a right angle . A right angle is half the size of the angle made by a straight line (180 ${}^{\circ }$ ). We say $CA$ is perpendicular to $AB$ or $CA\perp AB$ . An angle twice the size of a straight line is 360 ${}^{\circ }$ . An angle measuring 360 ${}^{\circ }$ looks identical to an angle of 0 ${}^{\circ }$ , except for the labelling. We call this a revolution . An angle of 90 ∘ is known as a right angle .

## Angles larger than 360 ${}^{\circ }$

All angles larger than 360 ${}^{\circ }$ also look like we have seen them before. If you are given an angle that is larger than 360 ${}^{\circ }$ , continue subtracting 360 ${}^{\circ }$ from the angle, until you get an answer that is between 0 ${}^{\circ }$ and 360 ${}^{\circ }$ . Angles that measure more than 360 ${}^{\circ }$ are largely for mathematical convenience.

• Acute angle : An angle $\ge {0}^{\circ }$ and $<{90}^{\circ }$ .
• Right angle : An angle measuring ${90}^{\circ }$ .
• Obtuse angle : An angle $>{90}^{\circ }$ and $<{180}^{\circ }$ .
• Straight angle : An angle measuring 180 ${}^{\circ }$ .
• Reflex angle : An angle $>{180}^{\circ }$ and $<{360}^{\circ }$ .
• Revolution : An angle measuring ${360}^{\circ }$ .

These are simply labels for angles in particular ranges, shown in [link] .

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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