Polygons are multi-sided shapes with different properties. Shapes have symmetrical properties and some can tessellate.

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A triangle is a 2D shape with three sides. There are four different triangles with different properties.

A **scalene triangle** has 3 sides of different lengths and 3 unequal angles.

An **isosceles triangle** has 2 sides of equal length. The dashes on the lines show they are equal in length. The angles at the base of the equal sides are equal.

An **equilateral triangle** has 3 sides of equal length. The dashes on the lines show they are equal in length. All of the angles are also equal.

A **right-angled triangle** is a triangle that has a right angle.

Letters can be used to label angles.

AB and AC are line segments, and they meet at point A. AB joins the points A and B.

The angle between AB and AC is labelled BAC.

The angle can written as BAC or BÂC or ∠BAC.

The angles inside a shape are called **interior angles**.

If the side of a triangle is extended, the angle formed outside the triangle is the **exterior angle**.

is the interior angle. is the exterior angle.

The interior angle and its corresponding exterior angle always add up to 180°.

The sum of interior angles in a triangle is 180°.

To prove , firstly draw a line parallel to one side of the triangle.

(alternate angles are equal)

(alternate angles are equal)

(angles on a straight line add up to 180°)

So .

These facts can be used to calculate angles.

- Question
Calculate the angles and .