1. 1-3 Measuring and constructing angles
Chapter 1
1-3 Measuring and constructing angles

2. Warm up Instructions: Answer the following questions
P1. M is between N and O. MO = 15, and MN = Find NO.
P2. S is the midpoint of TV, TS = 4x – 7, and
SV = 5x – 15. Find TS, SV, and TV.
P3. LH bisects GK at M. GM = 2x + 6, and
GK = 24. Find x.

3. Warm up Answers Instructions: Answer the following questions
P1. M is between N and O. MO = 15, and MN = Find NO.
Answer: 22.6
P2. S is the midpoint of TV, TS = 4x – 7, and
SV = 5x – 15. Find TS, SV, and TV.
Answer: 25,25,50
P3. LH bisects GK at M. GM = 2x + 6, and
GK = 24. Find x.
Answer: x=3

4. Objectives The students will be able to: * Name and classify angles.
*Measure and construct angles and angle
bisectors.

5. 1-3 Measuring and constructing Angles
What is an angle?
Answer: is a figure formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices).
How can we name an angle?
Answer: You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number.

6. 1-3 measuring and constructing angles
The set of all points between the sides of the angle is the interior of an angle. The exterior of an angle is the set of all points outside the angle.
Examples of naming angles can be:
Angle Name
R, SRT, TRS, or 1

7. 1-3 measuring and constructing angles
Example 1:
A surveyor recorded the angles formed by a transit (point A) and three distant points, B, C, and D. Name three of the angles.
Answer:BAC, CAD, BAD

8. 1-3 measuring and constructing angles
Example 2:
Name the following angles in three different ways

9. 1-3 measuring and constructing angles
The measure of an angle is usually given in degrees. Since there are 360° in a circle, one degree is 1/360 of a circle. When you use a protractor to measure angles, you are applying the following postulate:

10. 1-3 Measuring and constructing angles
You can use the Protractor Postulate to help you classify angles by their measure. The measure of an angle is the absolute value of the difference of the real numbers that the rays correspond with on a protractor.
If OC corresponds with c and OD corresponds with d,
mDOC = |d – c| or |c – d|.

11. 1-3 measuring and constructing angles
Example 3:
Example problem types
1.  Measure the following angles.  If necessary, continue the sides of the angle..
                            

12. 1-3 measuring AND CONSTRUCTING ANGLES
Example 3:
Measuring angles online
Measuring Angles with a Protractor - Welcome to Math Playground

13. 1-3 measuring and constructing angles

14. 1-3 measuring and constructing angles
Example 5:
Find the measure of each angle. Then classify each as acute, right, or obtuse.
A. WXV
mWXV = = 30°
WXV is acute.
B. ZXW
mZXW = |130° - 30°| = 100
ZXW = is obtuse

15. 1-3 measuring and constructing angles
What are congruent angles? Congruent angles are angles that have the same measure. In the diagram, mABC = mDEF, so you can write ABC  DEF. This is read as “angle ABC is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent.

16. 1-3 measuring and constructing angles

17. 1-3 measuring and constructing angles
Example 6:
Problem 1 from the angle addition postulate worksheet
1) Find 𝑚<𝐾𝐿𝑀 if 𝑚<𝐾𝐿𝐵 = 26°
and 𝑚<𝐵𝐿𝑀 = 60°.
Solution:
𝑚<𝐾𝐿𝑀=𝑚<𝐾𝐿𝐵+𝑚<𝐵𝐿𝑀 angle addition postulate
𝑚<𝐾𝐿𝑀= substitute values and simplify
𝑚<𝐾𝐿𝑀=86

18. 1-3 measuring and constructing angles
Example 7:
Problem 8 from the angle addition postulate worksheet
Find 𝑚<𝐼𝐻𝑄 if 𝑚<𝐼𝐻𝐺 = 176°and 𝑚<𝑄𝐻𝐺 = 130°.
Solution:
𝒎<𝑰𝑯𝑮=𝒎<𝑰𝑯𝑸+𝒎<𝑸𝑯𝑮 angle addition 176=x substitute values and solve
46=x

19. 1-3 measuring and constructing angles
Example 8
Problem 11 from the angle addition postulate worksheet
) 𝑚<𝐻𝐺𝐹 =16𝑥+ 4, 𝑚<𝐸𝐺𝐹 = 110°,and 𝑚<𝐻𝐺𝐸 =3𝑥+11. Find x.
Solution
𝑚<𝐻𝐺𝐹=𝑚<𝐸𝐺𝐹+𝐻𝐺𝐸 angle addition postulate
16𝑥+4=110+ 3𝑥+11 substitute vales and simplify
16𝑥+4=3𝑥+121 simplify
−3𝑥−4=−3𝑥−4 solve for x
13𝑥 13 =
X=9

20. 1-3 measuring and constructing angles
What is an angle bisector ?
Solution:
An angle bisector is a ray that divides an angle into two congruent angles.
JK bisects LJM; thus LJK  KJM.

21. 1-3 measuring and constructing angles
Example 9
Problem 13 from the angle bisector worksheet
Find x if 𝑚<2 =4𝑥+ 5 and 𝑚<1 =5𝑥− 2.
Solution
𝑚<1=𝑚<2 angle bisector
5𝑥−2=4𝑥+5 simplify and solve for x
−4𝑥+2 −4𝑥+2
X=7

22. Student guided practice
Do worksheet A
Do Worksheet B 2-8

23. Homework
Do problems 2-10 in your book page 24

24. Closure
Today we learned about naming and measuring the angles. We also learned about the angle addition postulate and the angle bisector. Tomorrow we are going to continue with lesson 1-4.