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Maths

Polygons

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A polygon is a 2-dimensional closed shape with straight sides. In this section we will revise the properties of polygons.

# Angle properties of triangles

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)

and

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.

Question

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°.

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