Simple Angles and Measuring Angles with a Protractor

Simple Angles, and Measuring Angles with a Protractor

When 2 lines, or 2 line segments meet, they form angles. Angles are named by 3 points (usually) but sometimes with just 1 point if the diagram is simple. Angle sizes are measured in degrees. A tool called a protractor measures degrees. Let’s look at the protractors first, and then we will try to measure these angles.

The angle on the left measures 50° Put the angle in the circle, and put the base line on the base line of the protractor. Determine where the angle line crosses the curve.

The angle on the right measures 130° Put the angle in the circle, and put the base line on the base line of the protractor. Determine where the angle line crosses the curve.

When 2 angles sum up to a straight line, they must add up to 180°. A straight line is actually an angle too, with a measurement of 180°. This angle is 50° This angle is 130°

An angle is described by three points, the center one is the angle. W Z X Y Measure angle ∠XYW in degrees ____ ° Measure angle ∠WYZ in degrees ____ ° Is ∠XYZ a straight line? Does ∠XYW + ∠WYZ = 180°?

An angle is described by three points, the center one is the angle. W Z X Y Measure angle ∠XYW in degrees 37° Measure angle ∠WYZ in degrees 143° Is ∠XYZ a straight line? YES! Does ∠XYW + ∠WYZ = 180°? YES!

Measure angle ∠ 213 in degrees _____ ° Measure angle ∠ 123 in degrees _____ ° 1 Measure angle ∠ 132 in degrees _____ ° Sum the total degrees of this triangle _____° 3 2 By rule, all triangles have exactly 180 degrees.

Measure angle ∠ 213 in degrees 28° Measure angle ∠ 123 in degrees 62° 1 Measure angle ∠ 132 in degrees 90° Sum the total degrees of this triangle: 180° 3 2 By rule, all triangles have exactly 180 degrees.

1 If an angle has a measure of 90°, it’s called a RIGHT ANGLE. A right angle is indicated by the little box in the corner. You do not have to measure angles with that box, they ARE 90°. If an angle is smaller than a right angle, it is an ACUTE ANGLE. Both angle 1 and angle 2 are both acute angles. 3 2

D P Q Measure angle ∠PDQ in degrees ____ ° Measure angle ∠DQP in degrees ____ ° Measure angle ∠DPQ in degrees ____ ° Total degrees in the whole triangle ____ °

D P Measure angle ∠PDQ in degrees 120° Measure angle ∠DPQ in degrees 30° Q Measure angle ∠DQP in degrees 30° Total degrees in the whole triangle 180° Angle ∠PDQ is MORE THAN 90°. Any angles greater than 90° is called an OBTUSE angle.

2 4 1 3 Measure angle ∠ 213 in degrees ____ ° THINK: Do Not Measure: ∠ 243 = ______° THINK: Do Not Measure: ∠ 123 = ____° THINK: Do Not Measure: ∠ 324 = ____° Measure angle ∠ 124 in degrees ____ °

2 93 1 58 4 90 90 3 Measure angle ∠ 213 in degrees 58° Measure angle ∠ 124 in degrees 93° THINK: Do Not Measure: ∠ 243 = 29° (58° + 93° + X° = 180° X° = 29°) THINK: Do Not Measure: ∠ 123 = 32° (90° + 58° + X° = 180° X° = 32°) THINK: Do Not Measure: ∠ 324 = 61° (93° - 32° = 61°)

6 9 Measure angle ∠ 678 in degrees ____ ° Measure angle ∠ 896 in degrees ____ ° Measure angle ∠ 789 in degrees ____ ° Measure angle ∠ 967 in degrees ____ ° What is the total number of degrees for the rectangle? ____ ° 7 8 Measure angle ∠ 978 in degrees ____ ° THINK: Do not measure ∠ 798 ____ ° THINK: Do not measure ∠ 679 ____ ° THINK: Do not measure ∠ 796 ____ ° A rectangle, or a square always has a total of ____ ° A triangle always has a total of ____ °

6 9 Measure angle ∠ 678 in degrees 90° Measure angle ∠ 896 in degrees 90° Measure angle ∠ 789 in degrees 90° Measure angle ∠ 967 in degrees 90° What is the total number of degrees for the rectangle? 360° 7 8 Measure angle ∠ 978 in degrees = 30° THINK: Do not measure ∠ 798 = 60° THINK: Do not measure ∠ 679 = 60° THINK: Do not measure ∠ 796 = 30° A rectangle, or a square always has a total of 360° A triangle always has a total of 180°.

6 30° 9 60° Measure angle ∠ 678 in degrees 90° Measure angle ∠ 896 in degrees 90° Measure angle ∠ 789 in degrees 90° Measure angle ∠ 967 in degrees 90° 60° What is the total number of degrees for the rectangle? 360° 90° 30° 7 8 Measure angle ∠ 978 in degrees = 30° THINK: Do not measure ∠ 798 = 60° THINK: Do not measure ∠ 679 = 60° THINK: Do not measure ∠ 796 = 30° A rectangle, or a square always has a total of 360° A triangle always has a total of 180°.

Homework A D H B E C F G

Homework Measure angle ∠A in degrees = 90° Measure angle ∠D in degrees = 90° H Measure angle ∠EFC in degrees = 90° A B C THINK: ∠ACF is degrees…. A rectangle has 360 ° in total. 90 + X =360 ∠ACF = 90° also. D E F G

Homework Measure angle ∠BEF in degrees = 63° and angle ∠G in degrees = 63° H THINK: ∠H is degrees = 54° (Total is 180 = 63 + X X = 54) A B C —————————— Measure angle ∠ABE in degrees 63° THINK: ∠EBC is degrees = 117° (63 + X = 180) Measure angle ∠FEB in degrees 63° THINK: ∠DEB is degrees = 117° (63 + X = 180) D E F G