Looking at 2D shapes - Geometry (Shape) by URBrainy.com - Free Printable

Problem Description:

The task is to analyze each 2D shape provided and describe its properties in terms of:
1. The number of acute angles (angles less than 90°).
2. The number of right angles (angles exactly 90°).
3. The number of obtuse angles (angles greater than 90° but less than 180°).
4. The number of lines of symmetry.

Let's solve this step by step for each shape.

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Shape 1: Rhombus

#### Description:
- A rhombus is a quadrilateral with all sides of equal length.
- Opposite angles are equal, and the diagonals bisect each other at right angles.

#### Analysis:
1. Acute angles: A rhombus can have either 2 acute angles or 0 acute angles, depending on its orientation. In this case, it has 2 acute angles.
2. Right angles: A rhombus does not have any right angles unless it is a square. Therefore, it has 0 right angles.
3. Obtuse angles: Corresponding to the acute angles, there are 2 obtuse angles.
4. Lines of symmetry: A rhombus has 2 lines of symmetry (along its diagonals).

#### Final Answer for Shape 1:
- Acute angles: 2
- Right angles: 0
- Obtuse angles: 2
- Lines of symmetry: 2

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Shape 2: Right Triangle

#### Description:
- A right triangle has one angle that is exactly 90° (a right angle).
- The other two angles are acute (each less than 90°).

#### Analysis:
1. Acute angles: There are 2 acute angles.
2. Right angles: There is 1 right angle.
3. Obtuse angles: A right triangle cannot have any obtuse angles. Therefore, it has 0 obtuse angles.
4. Lines of symmetry: A right triangle generally has 0 lines of symmetry unless it is an isosceles right triangle. In this case, it is not isosceles, so it has 0 lines of symmetry.

#### Final Answer for Shape 2:
- Acute angles: 2
- Right angles: 1
- Obtuse angles: 0
- Lines of symmetry: 0

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Shape 3: Regular Hexagon

#### Description:
- A regular hexagon is a polygon with 6 equal sides and 6 equal angles.
- Each internal angle of a regular hexagon is 120°.

#### Analysis:
1. Acute angles: A regular hexagon does not have any acute angles. Therefore, it has 0 acute angles.
2. Right angles: A regular hexagon does not have any right angles. Therefore, it has 0 right angles.
3. Obtuse angles: All internal angles of a regular hexagon are 120°, which are obtuse. Therefore, it has 6 obtuse angles.
4. Lines of symmetry: A regular hexagon has 6 lines of symmetry (3 through opposite vertices and 3 through the midpoints of opposite sides).

#### Final Answer for Shape 3:
- Acute angles: 0
- Right angles: 0
- Obtuse angles: 6
- Lines of symmetry: 6

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Shape 4: Irregular Pentagon

#### Description:
- This is an irregular pentagon (5-sided polygon) with varying side lengths and angles.
- From the image, we can observe the types of angles present.

#### Analysis:
1. Acute angles: There are 2 acute angles.
2. Right angles: There are 1 right angle.
3. Obtuse angles: There are 2 obtuse angles.
4. Lines of symmetry: This shape is irregular and asymmetrical, so it has 0 lines of symmetry.

#### Final Answer for Shape 4:
- Acute angles: 2
- Right angles: 1
- Obtuse angles: 2
- Lines of symmetry: 0

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Final Answers:

1. Rhombus:
- Acute angles: 2
- Right angles: 0
- Obtuse angles: 2
- Lines of symmetry: 2

2. Right Triangle:
- Acute angles: 2
- Right angles: 1
- Obtuse angles: 0
- Lines of symmetry: 0

3. Regular Hexagon:
- Acute angles: 0
- Right angles: 0
- Obtuse angles: 6
- Lines of symmetry: 6

4. Irregular Pentagon:
- Acute angles: 2
- Right angles: 1
- Obtuse angles: 2
- Lines of symmetry: 0

Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
\text{1. Rhombus: } \text{Acute: 2, Right: 0, Obtuse: 2, Symmetry: 2} \\
\text{2. Right Triangle: } \text{Acute: 2, Right: 1, Obtuse: 0, Symmetry: 0} \\
\text{3. Regular Hexagon: } \text{Acute: 0, Right: 0, Obtuse: 6, Symmetry: 6} \\
\text{4. Irregular Pentagon: } \text{Acute: 2, Right: 1, Obtuse: 2, Symmetry: 0}
\end{array}
}
\]