1. Measure and Classify Angles
1.4 Lesson
Measure and Classify Angles

2. Angle, Vertex, and Sides
an angle consists of two rays that share the same endpoint.
The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.

3. Naming Angles Name the three angles in diagram.
Name this one angle in 3 different ways.
WXY, WXZ, and YXZ
What always goes in the middle?
The vertex of the angle

4. Classifying Angles

5. EXAMPLE 1
Use the diagram to find the measure of the indicated angle. Then classify the angle a. b. c. d.
55 acute
125 obtuse
180 straight
90 right

6. Angle Addition Postulate
If D is in the interior of ABC, then
ABD +  DBC = ABC
Adding the 2 angle together gives you the big angle

7. ALGEBRA Given that m LKN =145 , find m LKM and m MKN.
EXAMPLE 2
Find angle measures o
ALGEBRA Given that m LKN =145 , find m LKM and m MKN.
SOLUTION
STEP 1
Write and solve an equation to find the value of x.
m LKN = m LKM + m MKN
Angle Addition Postulate
145 = (2x + 10) + (4x – 3) o
Substitute angle measures.
145 = 6x + 7
Combine like terms.
138 = 6x
Subtract 7 from each side.
23 = x
Divide each side by 6.

8. EXAMPLE 2
Find angle measures
STEP 2
Evaluate the given expressions when x = 23.
m LKM = (2x + 10)° = ( )° = 56°
m MKN = (4x – 3)° = (4 23 – 3)° = 89°
So, m LKM = 56° and m MKN = 89°.
ANSWER

9. Find the indicated angle measures.
GUIDED PRACTICE
Find the indicated angle measures.
Given that KLM is straight angle, find m KLN and m NLM.
SOLUTION
STEP 1
Write and solve an equation to find the value of x.
m KLM + m NLM
= 180°
Straight angle
(10x – 5)° + (4x +3)°
= 180°
Substitute angle measures.
14x – 2
= 180
Combine like terms.
14x
= 182
Subtract 2 from each side. x
= 13
Divide each side by 14.

10. GUIDED PRACTICE
STEP 2
Evaluate the given expressions when x = 13.
m KLM = (10x – 5)° = ( – 5)° = 125°
m NLM = (4x + 3)° = ( )° = 55°
ANSWER
m KLM
= 125°
m NLM
= 55°

11. GUIDED PRACTICE
Use the diagram shown below.
Identify all pairs of congruent angles in the diagram.
In the diagram,
Find the other angle measures in the diagram.
SOLUTION
A. There are two pairs of Congruent angles in the diagram.
T S and P Q ~
B. mQPR = 84 and mPTS = 121.

12. Angle Bisector A line which cuts an angle into two equal halves A
The blue ray on the right is the angle bisector of the angle on the left.
                                                     
The red ray on the right is the angle bisector of the angle on the left.
                                                              

13. Double an angle measure
EXAMPLE 3
Double an angle measure
In the diagram at the right, YW bisects XYZ, and m XYW = 18. Find m XYZ. o
SOLUTION
By the Angle Addition Postulate, m XYZ = m XYW + m WYZ. Because YW bisects XYZ you know that XYW WYZ. ~
So, m XYW = m WYZ, and you can write
M XYZ = m XYW + m WYZ = 18° + 18° = 36°.

14. Example 3
In the diagram below, YW bisects , and Find

15. Example 4