SUBSET OF LINES

SUBSET OF LINES, TYPES OF ANGLES

By Meneo Salvar

By Meneo Salvar

SUBSET OF LINES, TYPES OF ANGLES

By Meneo Salvar

DEFINED TERMS​

Ray-shares the property of a line, but it has a one

fixed point that stretches infinitely in one

direction only.

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Segment-It is a set of points on a line if and only

if it contains two points, called endpoints, and all

the points between them.chocolate bar’s

side can represent a segment.

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Types of Angles and Their Properties

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Acute Angle​-

More than 0° but

less than 90°​ in the protractor

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For example, given that

m∠DAC = (x + 4)°,

m∠CAB = 32°

m∠DAB = 53°​

To solve for x, we can use the formula:

m∠DAB = m∠DAC + m∠CAB.

Hence, we have:

53 = (x + 4) + 32

53 = x + 36

53 − 36 = x

x = 17°​

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​53°

​A

​B

​D

​C

​Therefore, we have:

m∠DAC = (x + 4)°

m∠DAC = (17 + 4)°

m∠DAC = 21°, an acute angle​

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Right Angle

Range of angle measurement:

Exactly 90°​

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On the figure given, there are 2

right angles: ∠HAE &∠EAB, and both are

equal to 90°.​

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​E

​A

​B

​H

​Obtuse Angle

​Range of angle measurement:

More than 90° but less than

180°

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A​

B​

F​

A​

G​

B​

Straight Angle

Range of angle measurement

Exactly 180°​

A straight angle is any angle that measures

exactly 180°, and looks exactly like a line. On

the figure above, the straight angle is

∠HAB or ∠BAH.​

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​H

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B

​A

Reflex Angle​

It is an angle

that is more than 180° but less than 360°.

You can normally find them objects with

large angles, such as a big slice of pizza. On

the image on the left, ∠GAL = 240°, hence, it is

considered as a reflex angle.​

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​

​G

​A

​L

Complete Angle​

is twice the measurement

of a straight angle. It measures exactly 360°,

or makes a full rotation. On the image on the

left, ∠LAD = 360°, therefore, it must be a

complete angle. One of the examples of a

complete angle is a clock’s minute and hour

hand completing a full clockwise rotation. ​

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full moon​

​D

L

​A

Select the best answer ​

1.While drawing the outline of Makati Park for your TLE project, you wanted to

know the perfect angle at which the grand fountain can be drawn. What

measuring instrument can you use to find the value of an angle in degrees?

A. Barometer C. Protractor

B. Compass D. Ruler

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1.Solution:

​Protractor

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​2.If ∠HAT is an acute angle, and it is congruent to ∠MAT, what type of angle is

∠MAT?

A. Right angle C. Obtuse angle

B. Acute angle D. Straight angle

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2.Solution:

​∠HAT is an acute angle ≅ ∠MAT, meaning same shape and size of angle

Therefore: ​∠MAT, is acute angle

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3.Given that m∠ORB = 13° and m∠BRY = 78°, and both angles share a common

ray RB , what type of angle is ∠ORY?

A. Right angle C. Obtuse angle

B. Acute angle D. Straight angle

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3.Solution:

13°​ +78°=91°

91° is obtuse angle​

​

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​R

R

​B

B

​Y

​O

​78°

13°

4.Given that ∠BOX is a straight angle, and OM is drawn from the center of

the straight angle, what type of angle is ∠BOM if ∠MOX is an obtuse

angle?

A. Right angle C. Obtuse angle

B. Acute angle D. Straight angle​

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​4.Solution;

​∠BOM= acute angle

∠MOX​= obtuse angle

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​M

​O

X

​B

​obtuse angle

acute angle

straight angle

5.Given that ∠TOS is a right angle with ray OP at the middle of the angle, ∠TOS

is the sum of two angles ∠TOP and ∠POS and ∠TOP ≅ ∠POS, find the value of a, if m∠TOP = 2a + 9

A. a = 18 C. a = 20

B. a = 19 D. a = 21​

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5.Solution:

​∠TOP=2A+9

45=2A+9

45-9=2A

36/2=2a/2

18=a​

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