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Maths

Polygons

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°.

image: triangle with angles marked a, b, c and d

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.

image: triangle with angles marked a, b, c and d

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.

image: triange with angles a and b labelled, one angle given as 70 degrees and an external angle in relation to b is given as 120 degrees

toggle answer

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°.

Back to Geometry and measures index

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