Introduction

Hello Year 5! Today, we’re going to learn about something very exciting in maths: the sum of the angles in a triangle.

What is a Triangle?

First, let’s remember what a triangle is. A triangle is a shape with three sides and three corners, which we call vertices.

The Key Rule

Now, here’s the key rule we need to learn:

No matter what type of triangle you have, the sum of all the angles inside it is always 180 degrees.

Why is this Important?

Knowing that all triangles add up to 180 degrees helps us solve many problems in maths, like finding missing angles!

Visualising Angles

Imagine a pizza cut into three slices. Each slice represents an angle in a triangle. When you add up the size of each slice, the entire pizza (triangle) is still the same size!

How to Find Missing Angles

If you know two angles in a triangle, you can find the third angle by using this formula:

$$

\text{Third Angle} = 180^\circ – (\text{Angle 1} + \text{Angle 2})

$$

Example

Let’s say you have a triangle with:

  • Angle 1 = 50 degrees
  • Angle 2 = 60 degrees

To find the third angle, you would calculate:

$$

\text{Third Angle} = 180^\circ – (50^\circ + 60^\circ)

$$

This means:

$$

\text{Third Angle} = 180^\circ – 110^\circ = 70^\circ

$$

So, the third angle is 70 degrees!

Tips and Tricks

  1. Use a protractor to measure angles accurately.
  2. Draw triangles and label the angles to practice.
  3. Remember: All triangles add up to 180 degrees.

Questions

Easy Level Questions

  1. What is the sum of the angles in a triangle?
  2. If one angle is 30 degrees and another is 60 degrees, what is the third angle?
  3. How many sides does a triangle have?
  4. What do we call the corners of a triangle?
  5. What is the measure of the angles in an equilateral triangle?
  6. If one angle is 90 degrees, what can you say about the other two angles in a right triangle?
  7. How many degrees are in a triangle?
  8. Can a triangle have two angles that are 45 degrees?
  9. If two angles are 20 degrees and 30 degrees, what is the third angle?
  10. What do we call a triangle with all angles equal?

Medium Level Questions

  1. In a triangle, one angle is 70 degrees and another is 50 degrees. What is the third angle?
  2. If a triangle has angles of 40 degrees and 100 degrees, what is the missing angle?
  3. What type of triangle has one angle greater than 90 degrees?
  4. Calculate the third angle if the first angle is 55 degrees and the second is 65 degrees.
  5. If a triangle has angles of 30 degrees, 60 degrees, and x degrees, what is x?
  6. Can a triangle have angles measuring 100 degrees, 40 degrees, and 50 degrees? Why?
  7. A triangle has two angles that are equal. If one angle is 40 degrees, what are the measures of the other two angles?
  8. What is the sum of angles in a triangle with angles measuring 80 degrees and 50 degrees?
  9. How would you draw a triangle with angles of 30, 60, and 90 degrees?
  10. If each angle in a triangle measures 60 degrees, what type of triangle is it?

Hard Level Questions

  1. In a triangle, one angle measures 2x, another measures x + 10, and the third angle is 3x. What is x?
  2. A triangle has angles of x, 2x, and 3x. What is the value of x?
  3. If two angles of a triangle are in the ratio 2:3 and the third angle measures 40 degrees, what are the measures of the first two angles?
  4. A triangle has angles measuring (3x – 10), (2x + 20), and (x + 10). Find the value of x.
  5. If a triangle’s angles are in the ratio 1:2:3, what are the angles?
  6. A triangle has one angle that is twice the size of another angle. If the smallest angle is x, what is the sum of all angles?
  7. In an isosceles triangle, the two equal angles are each (x + 20) degrees, and the third angle is x degrees. What is x?
  8. If the angles in a triangle are (5y + 10), (3y – 20), and (2y + 20), find y.
  9. A triangle has angles of (4x + 10), (2x + 20), and (x + 10). Calculate x.
  10. If one angle in a triangle is 10 degrees less than another angle, and the third angle is 20 degrees more than the first, what are the angles?

Answers and Explanations

Easy Level Answers

  1. 180 degrees.
  2. 90 degrees.
  3. Three sides.
  4. Vertices.
  5. 60 degrees each.
  6. Yes, the other two must add up to 90 degrees.
  7. 180 degrees.
  8. Yes, because 45 + 45 + 90 = 180.
  9. 130 degrees.
  10. Equilateral triangle.

Medium Level Answers

  1. 60 degrees.
  2. 40 degrees.
  3. Obtuse triangle.
  4. 60 degrees.
  5. 90 degrees.
  6. No, because 100 + 40 + 50 = 190, which is more than 180.
  7. 40 degrees each.
  8. 130 degrees.
  9. You would use a protractor to measure.
  10. Equilateral triangle.

Hard Level Answers

  1. x = 10 degrees.
  2. x = 10 degrees.
  3. 80 degrees and 120 degrees.
  4. x = 20 degrees.
  5. 30 degrees, 60 degrees, and 90 degrees.
  6. 180 – (x + 2x) = 180 – 3x.
  7. x = 20 degrees.
  8. y = 10 degrees.
  9. x = 20 degrees.
  10. The angles are 30, 40, and 50 degrees.

Great job, Year 5! Now you understand the sum of the angles in a triangle!