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Calculating angles | Year 6 Mathematics PDF Download
How to Calculate Angles
You can determine angles around straight lines by employing pattern-spotting, logic, and reasoning.
Key facts to remember:
- 360° constitutes a full turn
- 180° accounts for half a turn
Angles on a Straight Line
One half turn is 180°. When a straight line or half turn is split into two angles, knowing one angle enables the calculation of the other.
For instance, 120° + 60° = 180°.
If a straight line was divided into three angles, the sum of all three angles would be 180°.
Various examples of angles on straight lines illustrate how they sum up to 180°.
Example
Example: Can you work out what angle b is?
Sol:
Angle b, when on a straight line with 140°, must be 40°.
140° + 40° = 180°
For angle c, since b + c = 180°, and b is 40°, c equals 140°.
40° + 140° = 180°
Angle d is 40° as it's on a straight line with c.
c + d = 180°
Vertically Opposite Angles
- Vertically opposite angles refer to angles that are positioned opposite each other when a straight line intersects another straight line.
- These angles are always equal in measure.
Example
Example: What do you think angle c is in both of these diagrams?
In the first diagram angle c equals 70° and in the second diagram angle c equals 145°.
Angles b and d are vertically opposite, so they are equal too.
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FAQs on Calculating angles - Year 6 Mathematics
| 1. What are the different types of angles? |  |
Ans. The different types of angles include acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (more than 90 degrees but less than 180 degrees), and straight angles (exactly 180 degrees).
| 2. How do you calculate the measure of an angle? | |
Ans. To calculate the measure of an angle, you can use a protractor to measure the angle's opening in degrees. Alternatively, you can use trigonometric functions if you know the lengths of the sides of a triangle.
| 3. How can angles be classified based on their relationship to each other? | |
Ans. Angles can be classified as complementary angles (two angles that add up to 90 degrees), supplementary angles (two angles that add up to 180 degrees), adjacent angles (angles that share a common side and vertex), and vertical angles (opposite angles formed by intersecting lines).
| 4. What is the sum of interior angles in a triangle? | |
Ans. The sum of the interior angles in a triangle is always 180 degrees. This property is known as the Triangle Angle Sum Theorem.
| 5. How can you use angle properties to solve geometry problems? | |
Ans. Angle properties can be used to identify unknown angles in geometric shapes, determine the relationships between angles in a figure, and prove the congruence of triangles or other shapes. Understanding angle properties is essential for solving various geometry problems.
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Nov 23, 2024 Last updated |
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