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Chapter 5
Estimating &
Measuring Angles
Math 1202
MMC
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5.1 Estimating & Measuring Angles
Angles
 Angles are formed when two rays meet at a common point called a vertex.
 The two rays are called the arms of the angle.
 Angles are measured in degrees.
Types of angles:
1) Acute Angle:
An angle that measures less than 90º.
2) Right Angle:
An angle that measures 90º.
3) Obtuse Angle:
An angle that measures more than 90º but less than 180 º.
4) Straight Angle:
An angle that measures 180º.
5) Reflex Angle: An angle that measures more than 180º.
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Measuring Angles
 Protractors are used to measure angles.
 Protractors usually have two sets of measurements, so be careful of which one you use.
 Be sure you place the protractor on the angle correctly.
 The vertex of the angle should be on the origin , and the base line of the protractor on the
arm of the angle. (See below)
Angle measures 70º. So it is acute.
60
70
80
90
100
110
80 7
0
60
12
0
13
0
50
0
15
40
20
160
30
10
170
0
180
10
0
180 1
70
0
110 10
20
0 1
13
0
14
20
30
160
15
40
0
14
0
50
Ex)
Classify and estimate the measure of each angle. Use a protractor to find the achual
measurement.
Classification:______________________
Classification:_________________________
Estimate:
_____________________
Estimate:
_____________________
Actual:
_____________________
Actual:
_____________________
Classification:______________________
Classification:_________________________
Estimate:
_____________________
Estimate:
_____________________
Actual:
_____________________
Actual:
_____________________
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5.2 Angle Construction
1. Using a Protractor
 A protractor can be used to construct angles.
 Be sure you place the protractor properly when constructing angles.
The following steps shows how to construct an angle measuring 30º with a protractor





Your Turn:
Use a ruler to draw the base line
Place the protractor on the line as shown.
Mark a dot at 30º.
Draw a second arm to make the angle.
Label the size of the angle
Use a protractor to construct an angle measuring 125º
2) Set Squares
 There are two set squares (triangles)

Ex)
Use combinations of these set squares to draw the angle
Use set squares to construct the following angles
1) 135º
2)
120º
or
45°
30°
60°
60°
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Bisecting Angles
1) Using Paper folding
Draw the angle.
Fold through the vertex so
that one arm is placed on
top of the other arm.
Draw a line along the
fold line.
2) Using a Protractor- For example to bisect an angle measuring 50º.
 Divide the size of the angle by 2. (50 ÷ 2 = 25)
 Place a protractor so that the baseline is along one arm of the 50° angle. Mark a dot at
25°.

Draw a straight line from the dot to the vertex of the angle.
3) Using a compass and a straight edge
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5.3 Lines and angles
Types of Lines
1)



Parallel Lines
lines that do not (and will not) cross each other
are labeled using matching arrowheads
are always the same distance apart
2)
Transversal
 a line that crosses two or more parallel lines
3)
Perpendicular Lines
 lines that cross each other at right angles.
 often are marked with a right angle symbol.
Ex1 ) Identify each pair of lines as parallel, perpendicular or neither. Justify your answer.
A)
C)
B)
D)
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Pairs of angles
1)
2)
3)
Supplementary Angles
 two angles that add up to 180º
 they form a straight angle (line)


Complementary Angles
two angles that add up to 90º
they form a right angle.


Opposite Angles
a pair of angles formed by two lines that intersect.
these angles are equal in measure.
Ex 2) Determine the measure of each unknown angle.
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Page 250-251 #’s 1-7
Angles form with parallel lines and Transversals
1) Corresponding Angles
 angles that would fit on top of each other if you slide one of the parallel lines on top of
the other.
 Corresponding angles are equal.
 The diagram below shows 4 pairs of corresponding angles:
2)
3)



Alternate exterior Angles
Angles that are outside the parallel lines and on different sides of the transversal
Alternate exterior angles are equal.
The diagram below shows 2 pairs of alternate exterior angles:



Alternate interior Angles
Angles that are inside the parallel lines and on different sides of the transversal
Alternate interior angles are equal.
The diagram below shows 2 pairs of alternate interior angles:
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4)
5)
Ex)



Same side interior Angles
Angles that are inside the parallel lines and on same side of the transversal
Same side interior angles are supplementary. (add up to 180º)
The diagram below shows 2 pairs of same side interior angles:



Same side exterior Angles
Angles that are outside the parallel lines and on same side of the transversal
Same side exterior angles are supplementary. (add up to 180º)
The diagram below shows 2 pairs of same side exterior angles:
In the diagram below name a pair of:
A) Corresponding angles
B) Alternate exterior angles
C) Alternate interior angles
D) Same side interior angles
E) Same side exterior angles
F) If a  50  , find the measures of all the other angles:
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Assign pages 254-255 #’s 1-8 & Pages 258-259 #’s 1-7
5.4
Angles in Our world
You can use angle properties to determine if two lines cut by a transversal are parallel.
Remember if the lines are parallel then:
 Alternate interior angles are equal
 Alternate exterior angles are equal
 Corresponding angles are equal
 Same side interior angles are supplementary (add up to 180º)
 Same side exterior angles are supplementary (add up to 180º)
Ex)
Which lines are parallel? Give reasons for your answers.
60°
121°
59°
55°
Not parallel because corresponding
Are not equal
Parallel because same side interior angles
add up to 180º.
107°
95°
95°
101°
Not parallel because alternate exterior
Are not equal
62°
120°
Parallel because alternate interior
are equal
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Not parallel because same side interior angles
Add up to 182º, not 180º