Angle Addition and Bisector

Angles Measures and Relationships

Mr. Geraldo Banaag
FMS Geometry Honors
Sept 8-11, 2020

Fill in the Blank

Solve for x:

2x + 3 = x - 11

Fill in the Blank

Solve for x:

4x - 5 = 2x + 13

Objectives:

- Measure and classify angles. 
- Identify and use congruent angles and the bisector of an angle. 
- Use Protractor Postulate and the Angle Addition Postulate

Open Ended

How would you define an angle?

What properties can you share with the class about angles and its measure?

How do you think we can use the concept of angles in real-life?

Angles: Basic Terms

(Recall)

Measure Angles 

If two noncollinear rays have a common endpoint, they form an angle. The rays are the sides of the angle. The common endpoint is the vertex. The angle at the right can be named as ∠A, ∠BAC, ∠CAB, or ∠1.

Example:

a. Name all angles that have R as a vertex. 

b. Name the sides of ∠1. 

Congruent Angles 

Angles that have the same measure are congruent angles. A ray that divides an angle into two congruent angles is called an angle bisector. In the figure, PN is the angle bisector of ∠MPR. Point N lies in the interior of ∠MPR and ∠MPN ≅ ∠NPR.

Example:

Refer to the figure on the right. 
If m∠MPN = 2x + 14 and m∠NPR = x + 34, find x and find m∠NPR.

ALGEBRA

In the figure  QP and QR are opposite rays. 
QS bisects ∠PQT.       

If m∠PQT = 60 and m∠PQS = 4x + 14, find the value of x.

Fill in the Blank

If m∠PQS = 3x + 13 and m∠SQT = 6x – 2, find m∠PQT.

Multiple Choice

Name the vertex of ∠4.

• A

• B

• C

• D

Multiple Choice

In the figure BA and BC are opposite rays.

BF bisects ∠CBE.

If m∠3 = 6y + 2 and m∠4 = 8y – 14, find m∠CBF.

• 50

• 100

• 8