## Math 6 Chapter 2 Lesson 2: Angle

## 1. Summary of theory Tóm

**– Corner **is a figure consisting of two rays with a common origin. The common origin of two rays is called the vertex of the angle. The two rays are the two sides of the angle.

**– Sign: **\(\widehat {xOy};\,\,\,\widehat {yOx};\,\,\,\widehat O\)

**– Flat angle** is an angle whose sides are opposite rays.

**For example: **The angle xOy in the image above is a flat angle.

**– The point is in the corner**

- When the two rays Ox and Oy are not opposite, the point M is said to be in the angle xOy if the ray OM lies between the two rays Ox and Oy. Then the ray OM lies in the angle xOy.
- If ray OM lies in angle xOy then every point on ray OM lies in angle xOy.

## 2. Illustrated exercise

**Question 1: **Let’s give some actual pictures of corners, of flat corners.

– Some actual pictures of the angle: The angle formed by the hour and minute hands of the clock, the roof, the two sides of the ruler…

– Some pictures of flat corners such as: The double sheet of paper opens, the angle formed by the hour and minute hands at 6 o’clock; …

**Verse 2: **Let two lines x’x and y’y intersect at a point O. Know \(\widehat {xOy} = {45^0}\).

a) Calculate the angles \(\widehat {x’Oy};\,\,\,\widehat {x’Oy’};\,\,\widehat {xOy’}\).

b) Comment on the magnitude of the above angles.

**Guide to the solution**

a) Use the relationship between adjacent and complementary angles.

\(\widehat {x’Oy} = {135^0};\,\,\,\widehat {x’Oy’} = {45^0};\,\,\widehat {xOy’} = {135 ^0}\)

b) We have \(\widehat {xOy} = \,\,\widehat {x’Oy’};\,\,\widehat {x’Oy}\, = \widehat {xOy’}\)

Two straight lines intersect to form four angles, forming two pairs of equal angles.

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Given three common rays Ox, Oy, Oz. Know \(\widehat {xOy} = {30^0};\widehat {yOz} = {50^0}\). Calculate angle \(\widehat {xOz}?\).

**Verse 2:** Given two complementary adjacent angles xOy and yOz. We know that xOy has a measure greater than the measure of angle yOz by \({36^0}\). Calculate the measure of each angle.

**Question 3: **Given two complementary adjacent angles xOy, yOz. The measure of angle xOy is \(\frac{2}{7}\) the measure of angle yOz and the measure of angle xOz is \({153^0}\). Calculate the measure of each angle.

**Question 4: ** Given four rays Ox, Oy, Oz, Ot in that order and have the same origin O. Two rays Ox, Ot are opposite rays, \(\widehat {xOy} = {40^0}\) and \(\widehat {zOt} = {130^0}\).

a) Prove that the ray Oy is equal between the two rays Ox and Oz.

b) Calculate angle \(\widehat {yOz}\,\,\,\,?\)

**Question 5:** Five distinct rays with common origin O are OA, OB, OC, OD, OE forming consecutive adjacent angles. Know \(\widehat {AOB} = {30^0},\widehat {BOC} = {80^0},\widehat {COD} = {70^0},\widehat {DOE} = {30^0} \).

a) Know that A, O, D are collinear.

b) Calculate angle \(\widehat {EOA}\,\,?\)

c) Are the three points B, O, E collinear?

### 3.2. Multiple choice exercises Bài

**Question 1: **

Name the angles in the figure

A. \(\widehat {MON}\)

B. \(\widehat {MON},\widehat {NOP},\widehat {MOP}\)

C. \(\widehat {MON},\widehat {NOP}\)

D. \(\widehat {NOP},\widehat {MOP}\)

**Verse 2: **Name all the angles with one side Om in the figure

A. \(\widehat {xOm},\widehat {mOn}\)

B. \(\widehat {mOn}\)

C. \(\widehat {xOm},\widehat {mOn},\widehat {mOy},\widehat {xOy}\)

D. \(\widehat {xOm},\widehat {mOn},\widehat {mOy}\)

**Question 3: **Choose the wrong statement

A. A flat angle is an angle whose sides are opposite sides

B. Two angles are congruent if their measures are equal

C. An angle smaller than a right angle is a right angle

D. An obtuse angle is greater than a right angle

**Question 4: **Given 9 rays with a common origin (no rays overlap), the number of angles formed is

A. 16

B. 72

C. 36

D. 42

**Question 5: **Given the following figure:

Select the correct answers

A. \(\widehat {xOy}\) vertex O, edge Ox and Oy

B. \(\widehat {xyO}\) vertex O, edge Ox and Oy

C. \(\widehat {Oxy}\) vertex O, edge Ox and Oy

D. \(\widehat {xOy}\) vertex y, edge Ox and Oy

## 4. Conclusion

Through this lesson, you should be able to understand the following:

- Identify angles, flat angles.
- Understanding the point inside the angle.
- Know how to draw corners, name corners, read corner names.
- Identify the point in the corner.

.

=============

## Leave a Reply