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Measuring Angles
Chapter 1
Section 4
Common Core Standard: G.CO.1
Know precise definitions of angle, circle,
perpendicular line, parallel line, and line
segment based on the undefined notions
of point, line, distance along a line, and
distance around a circular arc.
Vocabulary
 Angle: Formed by 2 rays with the same endpoint.
 Sides: The rays of an angle.
 Vertex: The endpoint of an angle.
 Naming angles: there are 3 ways
 By the letter at the vertex.
 A letter on each side and the vertex. Vertex letter is the
middle letter.
 By a number inside the angle.
A
B
1
C
Vocabulary
 The interior of an angle is the region between the two
sides.
 The exterior of an angle is the region outside of the
two sides.
A
B
1
C
Vocabulary
 Acute angle: measures between 0 and 90 degrees
 Right Angles: Measures exactly 90 degrees
 Obtuse angle: Measures between 90 and 180 degrees
 Straight angle: Measures exactly 180 degrees
 Made of two opposite rays.
 Congruent Angles: Angles with the same measure
Protractor Postulate (1-7)
 This postulate allows you to measure an angle using a
protractor.
 The measure of an angle is the absolute value of the
difference of the real numbers paired with the two rays.
 IE: Take the number for each ray – subtract them – find
the absolute value.
Example 1
What is the measure of angle BOC? _____________
What is the measure of angle BOD? _____________
What is the measure of angle COA? _____________
What is the measure of angle DOC? _____________
Angle Addition Postulate (1-8)
 If point b is in the interior of AOC,
then m
AOB + m BOC = m AOC
 Meaning: If you have two adjacent angles you can add
the measure of the two angles to find the measure of the
large angle.
A
B
O
C
Example 2
A
4x - 20
If m AOC = 155,
find m AOB and m
B
3x + 14
O
C
BOC
Checkpoint
 Turn to page 31.
 With a partner – answer questions 1 – 5.
 You will have 8 minutes to complete this before we go
over.
Homework
 Pg 31# 6 – 20 even,
22, 23, 28, 29, 30, 42, 43