https://file.aiquickdraw.com/mathbot/file/1726070834669kmtzv51t.jpg

Let's go through the questions in the image and solve them one by one.

### 1.1 The supplement of 45° is:
The supplement of an angle is found by subtracting the angle from 180°.
\[
\text{Supplement of } 45° = 180° - 45° = 135°
\]
Answer: **135°**

### 1.2 60 is the ___________ of 20°
Here, it appears we need to find the relation between 60 and 20 in terms of multiplication, probably the multiple of 20 that equals 60.
\[
\frac{60}{20} = 3
\]
Thus, 60 is the **3rd multiple** of 20.

Answer: **third multiple**

### 1.3 __________ is the additive inverse of 7
The additive inverse of a number is the number that, when added to the original number, results in 0. The additive inverse of 7 is -7.
\[
7 + (-7) = 0
\]
Answer: **-7**

### 1.4 __________ is the multiplicative reciprocal of 4
The multiplicative reciprocal (or the inverse) of a number is found by dividing 1 by that number. The reciprocal of 4 is:
\[
\frac{1}{4}
\]
Answer: **\(\frac{1}{4}\)**

### 1.5 Simplify \(\sqrt{16x^2y^2}\)
We can simplify this square root by taking the square root of each part separately.
\[
\sqrt{16x^2y^2} = \sqrt{16} \cdot \sqrt{x^2} \cdot \sqrt{y^2} = 4xy
\]
Answer: **4xy**

### 1.6 Simplify \(\sqrt[3]{125p^3q^6r^9}\)
To simplify the cube root of this expression, we take the cube root of each part:
\[
\sqrt[3]{125p^3q^6r^9} = \sqrt[3]{125} \cdot \sqrt[3]{p^3} \cdot \sqrt[3]{q^6} \cdot \sqrt[3]{r^9}
\]
\[
= 5pq^2r^3
\]
Answer: **5pq²r³**

### 1.7 An angle of 360° is called?
An angle of 360° is called a **full angle** or a **complete angle**.
Answer: **full angle**

### 1.8 An equilateral triangle has three equal sides and angles, what is the size of one of the angles?
In an equilateral triangle, all three angles are equal. The sum of the angles in any triangle is 180°. Therefore, each angle in an equilateral triangle is:
\[
\frac{180°}{3} = 60°
\]
Answer: **60°**

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Do you want more details on any of these solutions?

Here are 5 relative questions to expand your knowledge:
1. What is the complement of a 45° angle?
2. How do you find the additive inverse of any number?
3. Can you explain how to find the reciprocal of a fraction?
4. What is the geometric interpretation of a full angle (360°)?
5. Why are all angles in an equilateral triangle equal?

**Tip:** When simplifying radicals, remember to take the square or cube root of each part individually to avoid mistakes!

The supplement of 45° is; 60 is the ___________ of 20°; __________ is the additive inverse of 7; __________ is the multiplicative reciprocal of 4; Simplify √(16x²y²); Simplify ³√(125p³q⁶r⁹); An angle of 360° is called?; An equilateral triangle has three equal sides and angles, what is the size of one of the angles?

Solve these math problems covering angles, additive inverses, multiplicative reciprocals, and simplification of radicals. Suitable for Grades 6-8 students, this exercise reinforces key algebraic and geometric concepts.

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