Count acute, obtuse, and right angles in each geometric shape on this educational worksheet.
Worksheet titled "Lines and Angles Worksheet #9" with eight geometric figures for counting acute, obtuse, and right angles.
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Step-by-step solution for: Grade 4 Maths Resources (8.1 Geometry - Revising Different Types ...
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Show Answer Key & Explanations
Step-by-step solution for: Grade 4 Maths Resources (8.1 Geometry - Revising Different Types ...
To solve the problem, we need to count the number of acute, obtuse, and right angles in each figure. Let's go through each figure step by step.
- Shape: A quadrilateral with intersecting diagonals.
- Analysis:
- Acute angles: There are 4 acute angles formed at the intersection of the diagonals.
- Obtuse angles: There are 4 obtuse angles formed at the intersection of the diagonals.
- Right angles: There are 0 right angles.
- Answer:
- Acute = 4
- Obtuse = 4
- Right = 0
- Shape: A pentagon with one diagonal.
- Analysis:
- Acute angles: There are 3 acute angles (at the top vertex and the two bottom vertices).
- Obtuse angles: There are 2 obtuse angles (at the two side vertices).
- Right angles: There are 0 right angles.
- Answer:
- Acute = 3
- Obtuse = 2
- Right = 0
- Shape: A rhombus with a horizontal line segment dividing it into two triangles.
- Analysis:
- Acute angles: There are 4 acute angles (two at the top and two at the bottom).
- Obtuse angles: There are 0 obtuse angles.
- Right angles: There are 4 right angles (where the horizontal line intersects the diagonals).
- Answer:
- Acute = 4
- Obtuse = 0
- Right = 4
- Shape: A circle.
- Analysis:
- Acute angles: There are 0 acute angles.
- Obtuse angles: There are 0 obtuse angles.
- Right angles: There are 0 right angles.
- Answer:
- Acute = 0
- Obtuse = 0
- Right = 0
- Shape: A trapezoid with a diagonal.
- Analysis:
- Acute angles: There are 2 acute angles (at the top vertices).
- Obtuse angles: There are 2 obtuse angles (at the bottom vertices).
- Right angles: There are 0 right angles.
- Answer:
- Acute = 2
- Obtuse = 2
- Right = 0
- Shape: A house-like shape with a triangular roof and a rectangular base.
- Analysis:
- Acute angles: There are 2 acute angles (at the top of the triangle).
- Obtuse angles: There are 0 obtuse angles.
- Right angles: There are 5 right angles (at the corners of the rectangle and where the triangle meets the rectangle).
- Answer:
- Acute = 2
- Obtuse = 0
- Right = 5
- Shape: A triangle with a smaller triangle on top.
- Analysis:
- Acute angles: There are 4 acute angles (two at the top triangle and two at the bottom triangle).
- Obtuse angles: There are 0 obtuse angles.
- Right angles: There are 0 right angles.
- Answer:
- Acute = 4
- Obtuse = 0
- Right = 0
- Shape: A quadrilateral with a diagonal.
- Analysis:
- Acute angles: There are 2 acute angles (at the top vertices).
- Obtuse angles: There are 2 obtuse angles (at the bottom vertices).
- Right angles: There are 0 right angles.
- Answer:
- Acute = 2
- Obtuse = 2
- Right = 0
\[
\boxed{
\begin{array}{ccc}
\text{Figure} & \text{Acute} & \text{Obtuse} & \text{Right} \\
1 & 4 & 4 & 0 \\
2 & 3 & 2 & 0 \\
3 & 4 & 0 & 4 \\
4 & 0 & 0 & 0 \\
5 & 2 & 2 & 0 \\
6 & 2 & 0 & 5 \\
7 & 4 & 0 & 0 \\
8 & 2 & 2 & 0 \\
\end{array}
}
\]
Figure 1:
- Shape: A quadrilateral with intersecting diagonals.
- Analysis:
- Acute angles: There are 4 acute angles formed at the intersection of the diagonals.
- Obtuse angles: There are 4 obtuse angles formed at the intersection of the diagonals.
- Right angles: There are 0 right angles.
- Answer:
- Acute = 4
- Obtuse = 4
- Right = 0
Figure 2:
- Shape: A pentagon with one diagonal.
- Analysis:
- Acute angles: There are 3 acute angles (at the top vertex and the two bottom vertices).
- Obtuse angles: There are 2 obtuse angles (at the two side vertices).
- Right angles: There are 0 right angles.
- Answer:
- Acute = 3
- Obtuse = 2
- Right = 0
Figure 3:
- Shape: A rhombus with a horizontal line segment dividing it into two triangles.
- Analysis:
- Acute angles: There are 4 acute angles (two at the top and two at the bottom).
- Obtuse angles: There are 0 obtuse angles.
- Right angles: There are 4 right angles (where the horizontal line intersects the diagonals).
- Answer:
- Acute = 4
- Obtuse = 0
- Right = 4
Figure 4:
- Shape: A circle.
- Analysis:
- Acute angles: There are 0 acute angles.
- Obtuse angles: There are 0 obtuse angles.
- Right angles: There are 0 right angles.
- Answer:
- Acute = 0
- Obtuse = 0
- Right = 0
Figure 5:
- Shape: A trapezoid with a diagonal.
- Analysis:
- Acute angles: There are 2 acute angles (at the top vertices).
- Obtuse angles: There are 2 obtuse angles (at the bottom vertices).
- Right angles: There are 0 right angles.
- Answer:
- Acute = 2
- Obtuse = 2
- Right = 0
Figure 6:
- Shape: A house-like shape with a triangular roof and a rectangular base.
- Analysis:
- Acute angles: There are 2 acute angles (at the top of the triangle).
- Obtuse angles: There are 0 obtuse angles.
- Right angles: There are 5 right angles (at the corners of the rectangle and where the triangle meets the rectangle).
- Answer:
- Acute = 2
- Obtuse = 0
- Right = 5
Figure 7:
- Shape: A triangle with a smaller triangle on top.
- Analysis:
- Acute angles: There are 4 acute angles (two at the top triangle and two at the bottom triangle).
- Obtuse angles: There are 0 obtuse angles.
- Right angles: There are 0 right angles.
- Answer:
- Acute = 4
- Obtuse = 0
- Right = 0
Figure 8:
- Shape: A quadrilateral with a diagonal.
- Analysis:
- Acute angles: There are 2 acute angles (at the top vertices).
- Obtuse angles: There are 2 obtuse angles (at the bottom vertices).
- Right angles: There are 0 right angles.
- Answer:
- Acute = 2
- Obtuse = 2
- Right = 0
Final Answer:
\[
\boxed{
\begin{array}{ccc}
\text{Figure} & \text{Acute} & \text{Obtuse} & \text{Right} \\
1 & 4 & 4 & 0 \\
2 & 3 & 2 & 0 \\
3 & 4 & 0 & 4 \\
4 & 0 & 0 & 0 \\
5 & 2 & 2 & 0 \\
6 & 2 & 0 & 5 \\
7 & 4 & 0 & 0 \\
8 & 2 & 2 & 0 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of angles worksheet geometry.