Angles PDF

What is an angle?  Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle. D E F  Here are...

What is an angle?  Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle. D E F  Here are some examples of angles  We can identify an angle by using a point on each ray and the vertex. The angle below may be identified as ∠ABC or ∠CBA or ∠B. The vertex point is always in the middle.  Naming Angles D E F B A G  Measuring Angles We measure the size of an angle using degrees. Here are some examples of angles and their degree measurements.  Congruent Angles Two angles that have the same measure are called congruent angles. A D 300 300 B E C F  Protractor A device used to measure angles. Reading a Protractor Which side of a protractor scale do you use? The easiest way to decide which scale to use is to look at the angle you're measuring. If it is greater than a right angle (more than ninety degrees) then use the scale that has numbers greater than 90. If the angle is less than a right angle (measures less than 90 degrees), use the scale which has numbers less than 90. Of course you have to line up the protractor correctly with the center point on the vertex of the angle and one of the rays of the angle coincide with the line on the protractor. Measuring, calculating and drawing angles... Our learning objectives today To use a protractor to: a) measure acute and obtuse angles to the nearest degree. b) draw acute and obtuse angles to the nearest degree. To calculate angles on a straight line.  What do we use to help us measure angles? A protractor These are standard protractors.  When we use a protractor, we need to line it up correctly with the angle. You need to make sure the protractor is lined up correctly. Is this ready to measure the angle? Is it right?............ it wasn’t! Look for the upside down ‘T’ in the middle of the straight line on your In this protractor look for protractor. the hole in the center. These spots need to be exactly on the vertex of your angle.  We also need to remember to line up the base One side of the angle must be lined up with the base of the protractor. It doesn’t matter which side. Kinds of Angles According to their Measures Acute Angles An acute angle is an angle measuring between 0 and 90 degrees. Examples: Obtuse Angles An obtuse angle is an angle measuring between 90 and 180 degrees. Example: Right Angles A right angle is an angle measuring exactly 90 degrees. Examples: Straight Angle  A straight angle is an angle measuring exactly 180 degrees. A perigon (or a revolution) is an angle that equals exactly 360º.  Reflex Angle A reflex angle is an angle which measures greater than 180º and less than 360º. Measuring Reflex Angles Now, we will use a protractor to measure the reflex angle PQR. To measure the reflex angle PQR, extend the arm PQ to A to form angle PQA which is a straight angle. Then measure the size of the angle AQR and add 180º.