Angle Measurements

Degrees: Measuring Angles We measure the size of an angle using degrees. Example: Here are some examples of angles and their degree measurements.

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 90 degrees, exactly. Examples:                                       

A perigon (or a revolution) is an angle that equals exactly 360º.

Reflex Angle A reflex angle is greater than 180º and less than 360º. It represents the largest amount of rotation.

Protractor A device used to measure angles.

Which side of a protractor scale do you use? 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. Happy measuring!

Measuring, calculating and drawing angles... Our learning objectives today To use a protractor to: measure acute and obtuse angles to the nearest degree. draw acute and obtuse angles to the nearest degree. To calculate angles on a straight line.

These are standard protractors. What do we use to help us? 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?

Were you right?............ it wasn’t! In this protractor look for the hole in the center. Look for the upside down ‘T’ in the middle of the straight line on your protractor. 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.

What does it measure? This angle measures 35°.

Now, we will use a protractor to measure the reflex angle PQR. 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.

Angle Bisector . D The bisector of an angle, also called the angle bisector is the ray, line or line segment that divides the angle into two equal parts.  

Complementary Angles Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. Example: These two angles are complementary. Their sum is 90˚.                                                        58° + 32° = 90°

Complementary Angles These two angles can be "pasted" together to form a right angle! Adjacent complementary angles.

Supplementary Angles Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees. Example: These two angles are supplementary. The sum of their measures is 180˚                                                                        139° +41° = 180 °

Linear Pair of Angles Special Supplementary Angles Two angles that share a vertex and a side to form a line. Two angles that can be "pasted" together to form a straight line!

Vertical Angles Opposite angles formed by intersecting lines .      For any two lines that meet, such as in the diagram below, angle AEB and angle DEC are called vertical angles. Angle BEC and angle AED are also vertical angles. Vertical angles are congruent - have the same degree measurement.           110 70 70 110

Review State whether the following are acute, right, or obtuse. 1. 3. 5. acute obtuse right 2. 4. ? acute obtuse ?

Complementary and Supplementary Find the missing angle. 1. Two angles are complementary. One measures 65 degrees. 2. Two angles are supplementary. One measures 140 degrees. Answer : 25 Answer : 40

Complementary and Supplementary Find the missing angle. You do not have a protractor. Use the clues in the pictures. 2. 1. x x 55 165 x = 180° – 165° x = 90° – 55° x = 15° x = 35 °

Vertical Angles Find the missing angle. You do not have a protractor. Use the clues in the pictures. x = 58 x 58

More drawings F E 20 70 90 Box in the corner indicates a right angle. J 20 H

Final Drawing B C 68 60 52 A G D 60 52 68 F E