Question

write three names for each angle.
1.
2.
3.
name three different angles for each diagram. (flipping the name will not count here.)
4.
5.
find the angle measure. then classify the angle.

1. m∠bod
2. m∠aoe
3. m∠coe
4. m∠cod

describe and correct the error in finding the angle measure. use the above diagram.

1. m∠boc = 25°
2. m∠doe = 65°

Explanation:

1. For the first - type of questions (writing three names for each angle):

An angle can be named in three common ways: by the vertex only (if there is no ambiguity), by the vertex and two points on the rays forming the angle, and by a number or letter assigned to the angle.

For the angle in question 1 with vertex \(B\):

• \(\angle B\) (using the vertex only)
• \(\angle ABC\) (using the vertex between two points on the rays)
• \(\angle 5\) (using the assigned number)

For the angle in question 2 with vertex \(G\):

• \(\angle G\)
• \(\angle FGH\)
• \(\angle 6\)

For the angle in question 3 with vertex \(K\):

• \(\angle K\)
• \(\angle JKL\)
• \(\angle 1\)

2. For the second - type of questions (naming three different angles for each diagram):

For question 4 with vertex \(M\):

• \(\angle HMK\)
• \(\angle KMN\)
• \(\angle HMN\)

For question 5 with vertex \(J\):

• \(\angle GJC\)
• \(\angle CJF\)
• \(\angle GJF\)

3. For the third - type of questions (finding angle measure and classifying the angle):

For \(m\angle BOD\):

• Read the measure from the protractor. The measure is \(120^{\circ}\). Since \(90^{\circ}<120^{\circ}<180^{\circ}\), it is an obtuse angle.

For \(m\angle AOE\):

• Read the measure from the protractor. The measure is \(140^{\circ}\). Since \(90^{\circ}<140^{\circ}<180^{\circ}\), it is an obtuse angle.

For \(m\angle COE\):

• Read the measure from the protractor. The measure is \(80^{\circ}\). Since \(0^{\circ}<80^{\circ}<90^{\circ}\), it is an acute angle.

For \(m\angle COD\):

• Read the measure from the protractor. The measure is \(40^{\circ}\). Since \(0^{\circ}<40^{\circ}<90^{\circ}\), it is an acute angle.

4. For the fourth - type of questions (describing and correcting the error in finding the angle measure):

For \(m\angle BOC = 25^{\circ}\) (error - description and correction):

• Error: If we assume the inner - scale of the protractor is used for measuring \(\angle BOC\), the reading is incorrect.
• Correction: By looking at the protractor, \(m\angle BOC=155^{\circ}\) (using the inner - scale as the ray \(OC\) and \(OB\) are considered, and starting the measurement from \(0^{\circ}\) on the inner - scale).

For \(m\angle DOE = 65^{\circ}\) (error - description and correction):

• Error: There is a mis - reading of the protractor.
• Correction: By looking at the protractor, \(m\angle DOE = 25^{\circ}\) (using the inner - scale for the rays \(OD\) and \(OE\)).

Answer:

1. \(\angle B\), \(\angle ABC\), \(\angle 5\)
2. \(\angle G\), \(\angle FGH\), \(\angle 6\)
3. \(\angle K\), \(\angle JKL\), \(\angle 1\)
4. \(\angle HMK\), \(\angle KMN\), \(\angle HMN\)
5. \(\angle GJC\), \(\angle CJF\), \(\angle GJF\)
6. \(120^{\circ}\), obtuse
7. \(140^{\circ}\), obtuse
8. \(80^{\circ}\), acute
9. \(40^{\circ}\), acute
10. Error: Incorrect protractor - reading. Correction: \(m\angle BOC = 155^{\circ}\)
11. Error: Incorrect protractor - reading. Correction: \(m\angle DOE=25^{\circ}\)