Certainly! Let's go through the problem step-by-step:
### Step 1: Understanding Complementary Angles
Complementary angles are two angles whose sum is always [tex]\(90^{\circ}\)[/tex].
### Step 2: Given Information
We are given that there is an angle of [tex]\(15^{\circ}\)[/tex] and its complementary angle. We are also given that the sum of the angle and its complementary angle results in [tex]\(100^{\circ}\)[/tex].
### Step 3: Finding the Complementary Angle
To find the complementary angle of [tex]\(15^{\circ}\)[/tex], we subtract [tex]\(15^{\circ}\)[/tex] from [tex]\(90^{\circ}\)[/tex]:
[tex]\[ \text{Complementary Angle} = 90^{\circ} - 15^{\circ} \][/tex]
By performing this calculation, we get:
[tex]\[ \text{Complementary Angle} = 75^{\circ} \][/tex]
### Step 4: Sum of the Given Angle and Its Complementary Angle
Now, we add the given angle [tex]\(15^{\circ}\)[/tex] and its complementary angle [tex]\(75^{\circ}\)[/tex]:
[tex]\[ \text{Sum of Angles} = 15^{\circ} + 75^{\circ} \][/tex]
By performing this addition, we get:
[tex]\[ \text{Sum of Angles} = 90^{\circ} \][/tex]
### Step 5: Analysis of the Given Condition
The problem states that the sum of the given angle and its complementary angle is [tex]\(100^{\circ}\)[/tex]. However, according to the mathematical definition and the calculations we performed:
[tex]\[ 15^{\circ} + 75^{\circ} = 90^{\circ} \][/tex]
Therefore, the given condition of the sum being [tex]\(100^{\circ}\)[/tex] appears to be an error.
### Conclusion
The complementary angle of [tex]\(15^{\circ}\)[/tex] is [tex]\(75^{\circ}\)[/tex]. The sum of [tex]\(15^{\circ}\)[/tex] and its complementary angle is [tex]\(90^{\circ}\)[/tex]. The given condition of the sum being [tex]\(100^{\circ}\)[/tex] is incorrect.
Final Results:
- Complementary angle: [tex]\(75^{\circ}\)[/tex]
- Sum of angles: [tex]\(90^{\circ}\)[/tex]
