Unit 5 Section 6 : Finding Angles in Triangles

Sum of the Interior Angles of a Triangle

The angles inside a triangle are called interior angles.
The diagram below shows the interior and exterior angles of a triangle.

The three interior angles in a triangle will always add up to 180°.

At each corner the exterior and interior angles are on a straight line, so at each corner these two angles add up to 180°.

Types of Triangle

When looking at the sides, there are three types of triangle: Isosceles, Equilateral and Scalene
Isosceles

An isosceles triangle has two lengths which are the same as each other, and two angles which are the same as each other.

Equilateral

An equilateral triangle has three equal lengths, and all the angles are equal which means they are each 60°.

Scalene

A scalene triangle has three different length sides, and three different angles.

Example Question

Work out the answer to the question then click on the button marked Click on this button below to see the correct answer to see whether you are correct.

Look at the triangle in the diagram below.

What is the size of missing angle a?

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
Find the unknown angle in each triangle.
(a) ? = °
(b) ? = °
(c) ? = °
(d) ? = °
(e) ? = °
(f) ? = °
Question 2
Find the unknown angles in each of the following triangles.
(a) a = °
b = °
(b) a = °
b = °
(c) a = °
b = °
c = °
(d) a = °
b = °
Question 3
State whether each triangle below is isosceles, equilateral or scalene.
(a)
(b)
(c)
(d)
Question 4
For each triangle below, find the unknown interior angle marked a and the exterior angle marked b.
(a) a = °
b = °
(b) a = °
b = °
(c) a = °
b = °
(d) a = °
b = °
Question 5
Look at the answers to the previous question.

How can you find the exterior angle at a third point using only the interior angles at the other two points?

Find the exterior angles marked on these triangles.
(a) ? = °
(b) ? = °
(c) ? = °
(d) ? = °

Question 6
Three exterior angles are marked a, b and c on the triangle below.
What is the total of the three exterior angles?

a + b + c = °

Question 7
Find the unknown angle or angles marked in each of the following diagrams.
(a) a = °
(b) a = °
(c) a = °
b = °
(e) a = °
b = °
c = °
d = °
(i) a = °
b = °
c = °
(l) a = °
b = °
c = °
d = °


You have now completed Unit 5 Section 6
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Produced by A.J.Reynolds April 2011