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Angles in triangles

All triangles have internal angles that sum up to 180°, regardless of the type of triangle.
Angles in triangles | Year 6 Mathematics

  • Isosceles Triangle: An isosceles triangle has two angles of the same size.
  • Equilateral Triangle: In an equilateral triangle, all angles are 60°.
  • Right-angled Triangle: This type of triangle has one 90° angle, making the other two angles add up to 90°.
  • Scalene Triangle: A scalene triangle has all angles of different sizes.

Examples

Example 1: How would you find two missing angles on an isosceles triangle?
Angles in triangles | Year 6 Mathematics

Use your knowledge about isosceles triangles - two angles are always the same size.
Find out what the total missing value is first:
180° - 50° = 130°
Angles d and e must now both equal 130°. Since we know these angles are both equal, you can find their value by halving 130°.
130° ÷ 2 = 65°
So d = 65° and e = 65°

Example 2: Look at this scalene triangle. How would you work out the value of a?
Angles in triangles | Year 6 Mathematics

Since you know that all angles in a triangle add up to 180°, you have to add up the values of the angles that you do know and then subtract them from 180°:
40° + 60° = 100°
180° - 100° = 80°
Therefore:
a = 80°

Angles on a Straight Line

  • Angles on a straight line add up to 180°.
  • If a straight line is divided into multiple angles, treat it like angles of a triangle put together.
  • To find a missing angle on a straight line, add the known angles together.
  • Subtract the sum of known angles from 180° to find the missing angle.
  • For instance, if you know two angles are 90° and 35°, the missing angle would be 55°.
    Angles in triangles | Year 6 Mathematics
The document Angles in triangles | Year 6 Mathematics is a part of the Year 6 Course Year 6 Mathematics.
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FAQs on Angles in triangles - Year 6 Mathematics

1. What is the relationship between the angles in a triangle?
Ans. In a triangle, the sum of the three interior angles always adds up to 180 degrees.
2. How can we find the measure of an unknown angle in a triangle?
Ans. To find the measure of an unknown angle in a triangle, we can use the fact that the sum of the three interior angles is always 180 degrees. By subtracting the measures of the two known angles from 180 degrees, we can find the measure of the unknown angle.
3. Can a triangle have two right angles?
Ans. No, a triangle cannot have two right angles because the sum of the interior angles of a triangle must always be 180 degrees. If two angles are right angles (each measuring 90 degrees), the third angle would have to be 0 degrees, which is not possible in a triangle.
4. How do angles on a straight line relate to triangles?
Ans. Angles on a straight line add up to 180 degrees. This property can be useful when calculating angles in triangles, as the straight line can be considered as the base of the triangle.
5. Why is it important to understand angles in triangles?
Ans. Understanding angles in triangles is important in geometry as it helps in solving various problems related to shapes and measurements. It is a fundamental concept that forms the basis for more advanced geometric calculations and proofs.
54 videos|54 docs|17 tests
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