Answer :
Certainly! Let's break down each part of the question step by step:
### Part 1: Finding All Angles of a Parallelogram
Given one angle of a parallelogram is 80°.
1. Identifying Relationships:
- In a parallelogram, opposite angles are equal.
- Adjacent angles are supplementary, meaning they add up to 180°.
2. Calculating the Adjacent Angle:
- Since one angle is 80°, the adjacent angle would be \(180° - 80° = 100°\).
3. Finding the Other Angles:
- The other angles will be:
- Opposite of 80° is also 80°.
- Opposite of 100° is also 100°.
Thus, the four angles of the parallelogram are:
[tex]\[80°, 100°, 80°, 100°.\][/tex]
### Part 2: Measuring the Acute Angle Between the Diagonals of a Rectangle
Given inclination of one diagonal to one of its sides is 25°.
1. Understanding the Properties:
- In a rectangle, diagonals bisect each other and are equal in length.
- When one diagonal is inclined to a side at a certain angle, the other angle made with the other diagonal forms an isosceles triangle.
2. Calculating the Acute Angle:
- If one diagonal forms a 25° inclination, the acute angle between the two diagonals will be twice this inclination (since both halves of the isosceles triangle share the same angle).
- Therefore, the acute angle between the diagonals will be:
[tex]\[25° \times 2 = 50°.\][/tex]
Combining both parts, we have:
1. Parallelogram Angles:
[tex]\[80°, 100°, 80°, 100°.\][/tex]
2. Acute Angle between Diagonals of Rectangle:
[tex]\[50°.\][/tex]
These are the final answers for the given questions.
### Part 1: Finding All Angles of a Parallelogram
Given one angle of a parallelogram is 80°.
1. Identifying Relationships:
- In a parallelogram, opposite angles are equal.
- Adjacent angles are supplementary, meaning they add up to 180°.
2. Calculating the Adjacent Angle:
- Since one angle is 80°, the adjacent angle would be \(180° - 80° = 100°\).
3. Finding the Other Angles:
- The other angles will be:
- Opposite of 80° is also 80°.
- Opposite of 100° is also 100°.
Thus, the four angles of the parallelogram are:
[tex]\[80°, 100°, 80°, 100°.\][/tex]
### Part 2: Measuring the Acute Angle Between the Diagonals of a Rectangle
Given inclination of one diagonal to one of its sides is 25°.
1. Understanding the Properties:
- In a rectangle, diagonals bisect each other and are equal in length.
- When one diagonal is inclined to a side at a certain angle, the other angle made with the other diagonal forms an isosceles triangle.
2. Calculating the Acute Angle:
- If one diagonal forms a 25° inclination, the acute angle between the two diagonals will be twice this inclination (since both halves of the isosceles triangle share the same angle).
- Therefore, the acute angle between the diagonals will be:
[tex]\[25° \times 2 = 50°.\][/tex]
Combining both parts, we have:
1. Parallelogram Angles:
[tex]\[80°, 100°, 80°, 100°.\][/tex]
2. Acute Angle between Diagonals of Rectangle:
[tex]\[50°.\][/tex]
These are the final answers for the given questions.
