MEASURING ANGLES WITH A PROTRACTOR

In order to measure angles we use a protractor with tiny 1^o markings on it.

To use a protractor to measure angles we:

place it so its centre is at the angle’s vertex and 0o lies exactly on one arm
start at 0^o and follow the direction the angle turns through to reach the other arm

The angle at Q is written as PQR or RQP. Notice that Q is in the middle.

This method of writing angles is called three point notation. The figure alongside shows why three point notation is essential.

If we say ‘the angle at D’ we could be referring to ADB, b ADC or BDC

What is the size of the angle being measured ?

Problem 1 :

Solution :

The angle AOB is 47°.

Problem 2 :

Solution :

The angle AOB is 123°.

Problem 3 :

Solution :

The angle AOB is 60°.

Problem 4 :

Solution :

The angle AOB is 75°.

Problem 5 :

Solution :

The angle AOB is 123°.

Problem 6 :

Solution :

The angle AOB is 84°.

Problem 7 :

Solution :

The angle AOB is 26°.

Problem 8 :

Solution :

The angle AOB is 23°.

Problem 9 :

Draw a diagram to illustrate:

i) a 1/2 turn

ii) a 1/4 turn

iii) a full turn

Solution :

i) A half turn

ii) One fourth turn

iii)

Problem 10 :

Name the following angles in three point notation. State the type of angle in each case

Solution :

∠ABC and ∠CBA

Type of angle : Acute angle

ii)

Solution :

∠PQR and ∠RQP

Type of angle : Obtuse angle

iii)

Solution :

Reflexive of ∠KLM or Reflexive of ∠MLK

Problem 11 :

Measure all angles of the following figures. Use three point notation to write down your answers.

Solution :

∠BAC = 83^o, ∠ACB = 31^o, ∠ABC = 66^o

ii)

Solution :

∠FDE = 119^o, ∠DEF = 32^o, ∠DFE = 29^o

iii)

Solution :

∠ABC = 94^o, ∠BCD = 78^o, ∠CDA = 78^o, ∠DAB = 110^o

iv)

Solution :

∠PQR = 54^o, ∠QRS = 127^o, ∠RST = 127^o, ∠STP = 91^o,
∠TPQ = 141^o

MEASURING ANGLES WITH A PROTRACTOR

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