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### 2.4 What is the supplement of [tex]\(125^\circ\)[/tex]?
- Step 1: Understand that supplementary angles sum up to [tex]\(180^\circ\)[/tex].
- Step 2: To find the supplement of [tex]\(125^\circ\)[/tex], subtract [tex]\(125^\circ\)[/tex] from [tex]\(180^\circ\)[/tex].
[tex]\[ \text{Supplement of } 125^\circ = 180^\circ - 125^\circ = 55^\circ \][/tex]
So, the supplement of [tex]\(125^\circ\)[/tex] is [tex]\(55^\circ\)[/tex].
### 2.5 How many degrees is a revolution?
- Revolution Definition: A full revolution indicates a complete turn around a circle.
- Degrees in a Circle: A complete circle is measured to be [tex]\(360^\circ\)[/tex] in terms of degrees.
Therefore, a full revolution is [tex]\(360^\circ\)[/tex].
### 2.6 How many degrees is a straight angle?
- Straight Angle Definition: A straight angle forms a straight line.
- Measurement: A straight line or angle is always measured to be [tex]\(180^\circ\)[/tex].
Thus, a straight angle is [tex]\(180^\circ\)[/tex].
### 2.7 If two obtuse angles are added together, what is the maximum size the angle can be?
- Obtuse Angle Definition: An obtuse angle is one that is greater than [tex]\(90^\circ\)[/tex] but less than [tex]\(180^\circ\)[/tex].
- Maximum Size Calculation: To find the maximum size of two obtuse angles combined:
- Considering both angles to be just under [tex]\(180^\circ\)[/tex].
Maximum sum of two obtuse angles:
[tex]\[ 179^\circ + 179^\circ = 358^\circ \][/tex]
Hence, the maximum size of two obtuse angles added together is [tex]\(358^\circ\)[/tex].
### 2.8 If two reflex angles are added together, what is the maximum size the angle can be?
- Reflex Angle Definition: A reflex angle is one that is greater than [tex]\(180^\circ\)[/tex] but less than [tex]\(360^\circ\)[/tex].
- Maximum Size Calculation: To find the maximum size of two reflex angles combined:
- Considering both angles to be just under [tex]\(360^\circ\)[/tex].
Maximum sum of two reflex angles:
[tex]\[ 359^\circ + 359^\circ = 718^\circ \][/tex]
Thus, the maximum size the sum of two reflex angles can be is [tex]\(718^\circ\)[/tex].
### Summary of Answers
- 2.4: The supplement of [tex]\(125^\circ\)[/tex] is [tex]\(55^\circ\)[/tex].
- 2.5: A revolution is [tex]\(360^\circ\)[/tex].
- 2.6: A straight angle is [tex]\(180^\circ\)[/tex].
- 2.7: The maximum size two added obtuse angles can be is [tex]\(358^\circ\)[/tex].
- 2.8: The maximum size two added reflex angles can be is [tex]\(718^\circ\)[/tex].
### 2.4 What is the supplement of [tex]\(125^\circ\)[/tex]?
- Step 1: Understand that supplementary angles sum up to [tex]\(180^\circ\)[/tex].
- Step 2: To find the supplement of [tex]\(125^\circ\)[/tex], subtract [tex]\(125^\circ\)[/tex] from [tex]\(180^\circ\)[/tex].
[tex]\[ \text{Supplement of } 125^\circ = 180^\circ - 125^\circ = 55^\circ \][/tex]
So, the supplement of [tex]\(125^\circ\)[/tex] is [tex]\(55^\circ\)[/tex].
### 2.5 How many degrees is a revolution?
- Revolution Definition: A full revolution indicates a complete turn around a circle.
- Degrees in a Circle: A complete circle is measured to be [tex]\(360^\circ\)[/tex] in terms of degrees.
Therefore, a full revolution is [tex]\(360^\circ\)[/tex].
### 2.6 How many degrees is a straight angle?
- Straight Angle Definition: A straight angle forms a straight line.
- Measurement: A straight line or angle is always measured to be [tex]\(180^\circ\)[/tex].
Thus, a straight angle is [tex]\(180^\circ\)[/tex].
### 2.7 If two obtuse angles are added together, what is the maximum size the angle can be?
- Obtuse Angle Definition: An obtuse angle is one that is greater than [tex]\(90^\circ\)[/tex] but less than [tex]\(180^\circ\)[/tex].
- Maximum Size Calculation: To find the maximum size of two obtuse angles combined:
- Considering both angles to be just under [tex]\(180^\circ\)[/tex].
Maximum sum of two obtuse angles:
[tex]\[ 179^\circ + 179^\circ = 358^\circ \][/tex]
Hence, the maximum size of two obtuse angles added together is [tex]\(358^\circ\)[/tex].
### 2.8 If two reflex angles are added together, what is the maximum size the angle can be?
- Reflex Angle Definition: A reflex angle is one that is greater than [tex]\(180^\circ\)[/tex] but less than [tex]\(360^\circ\)[/tex].
- Maximum Size Calculation: To find the maximum size of two reflex angles combined:
- Considering both angles to be just under [tex]\(360^\circ\)[/tex].
Maximum sum of two reflex angles:
[tex]\[ 359^\circ + 359^\circ = 718^\circ \][/tex]
Thus, the maximum size the sum of two reflex angles can be is [tex]\(718^\circ\)[/tex].
### Summary of Answers
- 2.4: The supplement of [tex]\(125^\circ\)[/tex] is [tex]\(55^\circ\)[/tex].
- 2.5: A revolution is [tex]\(360^\circ\)[/tex].
- 2.6: A straight angle is [tex]\(180^\circ\)[/tex].
- 2.7: The maximum size two added obtuse angles can be is [tex]\(358^\circ\)[/tex].
- 2.8: The maximum size two added reflex angles can be is [tex]\(718^\circ\)[/tex].
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