🎯 In this topic you will

• Find the sum of the angles in a triangle.
• Use the sum of the angles in a triangle to work out missing angles.

🧠 Think like a Mathematician

Question: What happens when the three angles of a triangle are placed together along a straight line?

Equipment: Paper, ruler, scissors

Method:

1. Draw a triangle on a piece of paper. The triangle can be any size, but use a ruler to draw the sides.
2. Mark each angle of the triangle using arcs.
3. Carefully cut out the triangle using scissors.
4. Draw a straight horizontal line in your book.
5. Tear off the three corners (angles) of the triangle.
6. Place the three angles next to each other along the straight line so that their points meet.

Follow-up Questions:

❓ EXERCISES

1. Work out angle $x$ in each of these triangles.

👀 Show answer

a. $x = 60^\circ$

b. $x = 50^\circ$

c. $x = 20^\circ$

2. Work out angle $y$ in each of these triangles.

👀 Show answer

a. $y = 50^\circ$

b. $y = 70^\circ$

3. This is part of Filipe’s homework. His homework is correct.

Question: This triangle is isosceles. Work out angles $a$ and $b$.

👀 Show answer

$a = 50^\circ$

$b = 80^\circ$

4. Work out angle $z$ in each of these triangles.

👀 Show answer

a. $z = 124^\circ$

b. $z = 66^\circ$

5. Show that angle $m$ in this triangle is $27^\circ$.

👀 Show answer

$m = 27^\circ$

6. The diagram shows the roof of Alice’s house. The angle marked $p$ needs to be at least $15^\circ$. Can she use the special tiles?

👀 Show answer

$p = 17^\circ$ so she can use the tiles.

7. Arun and Marcus work out the size of the angles in an equilateral triangle.

a. Who is correct?

b. Show that the correct person is right.

👀 Show answer

Marcus is correct. In an equilateral triangle the angles are equal and sum to $180^\circ$, so each angle is $60^\circ$.

8. The cards show the sizes of two angles of triangles $A$ to $I$. Sort these triangles into groups.

👀 Show answer

Equilateral: $I$

Isosceles: $B, D$

Scalene: $A, C, F, H$

Right-angled: $E, G$

9. The diagram shows a triangle on a straight line.

a. Which rule can you use to work out angle $a$?

b. Work out the size of angle $a$.

c. Work out the size of angle $b$.

👀 Show answer

a. Angles on a straight line add to $180^\circ$.

b. $a = 53^\circ$

c. $b = 43^\circ$