1.3 Measuring Angles

Lesson Essential Question: How do you accurately measure angles and use the Angle Addition Postulate?

Bellringer

1.) Which "Building Block of Geometry" term would accurately describe the two hands on a clock?

a) line segmentb) anglec) rayd) point

2.) The distance from town A to town C is 50 miles. Town B is in between towns A and C. The distance from town A to town B is 22 miles. What is the distance from town B to town C?

a) 72 milesb) 30 milesc) 28 milesd) 38 miles

Four Types of Angles

Right Angle Definition

Example

Acute Angle

Obtuse Angle

Straight Angle

What are the steps to measuring an angle?

1. Use a protractor (which is used to measure angles).2. Put the center of the protractor at the vertex. (where the two rays meet)3. Align the protractor so that the bottom ray passes through 0 on the protractor.4. Read the measure of the angle (using the appropriate scale) at the point where the other ray intersects the protractor.

Construct the following angles·Remember the directions on how to construct angles using a

protractor...

1. m ABC = 35 2. m DEF = 90

3. m YXZ = 108 4. m MNP = 180

Congruent Angles

Which angles are ≅ ?

Angle Congruence Postulate (1.3.2) If two (2) angles have the same measure, then they arecongruent. If two (2) angles are congruent, then they have thesame measure.

A

C

B

D

Bellringer

Write an example of a acute, obtuse, right, and straight angle

Angle Addition Postulate (1.3.3)If point S is in the interior of PQR then m PQS + m

SQR = m PQR

VISUAL EXAMPLE

Independent Practice

B E

M

T

If m BTM = 39, m BTE = (3x - 6) , and m ETM = (x + 25) , then find the following...

1.) What is the value of x? ______________________

2.) What is the m BTE? _______________________

Special Angle Pairs (1.3.4) Complimentary angles are 2 angles whose measures have a sum of 90 . Each angle is called the complement of the other.

Example

Supplementary angles are 2 angles whose measures have a sum of 180 . Each angle is called the supplement of the other.

Example

If the endpoint of a ray falls on a line so that 2 angles are formed, then the angles are known as a linear pair.

1 and 2 form a linear pair.

Linear Pair Property (1.3.5) If 2 angles form a linear pair, then they are supplementary.

EXAMPLE

1 2

(2x + 24)(6x - 2)