Intro to Angle Measurement 1.4 Angles and Their Measures Intro to Angle Measurement

Measuring Angles Angles are measured using a protractor, which looks like a half-circle with markings around its edges. Angles are measured in units called degrees 45 degrees, for example, is symbolized like this: Every angle measures more than 0 degrees and less than or equal to 180 degrees.

A Protractor

The smaller the opening between the two sides of an angle, the smaller the angle measurement. The largest angle measurement (180 degrees) occurs when the two sides of the angle are pointing in opposite directions. To denote the measure of an angle we write an “m” in front of the symbol for the angle.

Here are some common angles and their measurements. 1 2 4 3

Note – Geometry doesn’t use equal signs like Algebra MEASURES ARE EQUAL mBAC = mDEF ANGLES ARE CONGRUENT BAC  DEF “is congruent to” “is equal to” Note that there is an m in front when you say equal to; whereas the congruency symbol  ; you would say congruent to. (no m’s in front of the angle symbols).

Types of Angles An acute angle is an angle that measures less than 90 degrees. A right angle is an angle that measures exactly 90 degrees. An obtuse angle is an angle that measures more than 90 degrees. acute right obtuse

A straight angle is an angle that measures 180 degrees A straight angle is an angle that measures 180 degrees. (It is the same as a line.) When drawing a right angle we often mark its opening as in the picture below. right angle straight angle

Angles and Their Parts An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex of the angle.

Note: The measure of A is denoted by mA. The measure of an angle can be approximated using a protractor, using units called degrees(°). For instance, BAC has a measure of 50°, which can be written as mBAC = 50°. B A C

Reading a protractor. A O B What is the measure of angle BOA? 113°

1.4 Angles and their Measures

“angle A” “angle BAC” “angle CAB” Angles Or, you can use 3 points on the angle with the vertex in the middle… You can use the vertex of an angle to name it… “angle A” “angle BAC” “angle CAB”

How many angles do you see? Naming Angles How many angles do you see?

Three angles!

PQS and SQR are adjacent. Adjacent Angles PQS and SQR are adjacent.

Interior vs. Exterior

Measuring Angles A protractor is used to find the measure of an angle. “The measure of angle BAC is 50 degrees.”

Angle Addition Postulate + =

Example: Calculating Angle Measures VISION. Each eye of a horse wearing blinkers has an angle of vision that measures 100°. The angle of vision that is seen by both eyes measures 60°. Find the angle of vision seen by the left eye alone.

Solution: You can use the Angle Addition Postulate.

A B “Two angles are congruent if and only if they have the same measure”

Classifying Angles classification example measure range