A polygon is a 2-dimensional closed shape with straight sides. In this section we will revise the properties of polygons.
We already know that the angles in a triangle add up to 180°. Angles on a straight line also add up to 180°.
In the diagram, we see that:
a + b + c = 180° (angles in a triangle)
c + d = 180° (angles on a straight line).
If we rearrange both equations (subtract c from both sides), we get:
a + b = 180° - c and d = 180° - c.
Therefore, a + b and d must be the same (they are both equal to 180° - c):
a + b = d
Now look again at the diagram.
The exterior angle is equal to the sum of the two opposite interior angles.
This is true for any triangle.
Find each angle marked with a letter, giving reasons for your answer.
Did you get the answer a = 50°? The exterior angle (120°) is equal to the sum of the two opposite interior angles (70° + a).
Therefore, 70° + a = 120°, so a = 50°.
b = 60°, because the angles on a straight line add up to 180°.
b + 120° = 180°, so b = 60°.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.