Polygons and regions

A triangle is a polygon with three sides. The sides connect the points called vertices.

A right-angled triangle has one angle equal to $90^{\circ}$.

An isosceles triangle has two equal sides and two equal angles.

An equilateral triangle has three equal sides and all angles equal.

A triangle with all sides different and all angles different is called a scalene triangle.

A triangle with vertices $A$, $B$ and $C$ is denoted as $\triangle ABC$.

A triangle has two kinds of angles:

1. Interior angles
2. Exterior angles

Interior angle – is an angle inside the triangle. The sum of interior angles of a triangle is $180^{\circ}$.

Example, consider the triangle below.

Exterior angle – is an angle outside the triangle. Consider the triangle below.

Find the angles $x$ and $y$ in the diagrams below.

A quadrilateral is a polygon with four sides. Examples of quadrilaterals are a square, a rectangle, a rhombus, a parallelogram, a kite and a trapezium.

A square has equal sides and all angles are $90^{\circ}$.

A rectangle has two pairs of opposite sides equal and all angles are $90^{\circ}$.

A rhombus has all sides equal. Opposite angles are also equal.

A parallelogram has two pairs of opposite sides equal. Opposite angles are also equal.

A kite has two pairs of adjacent sides equal. One pair of opposite angles are also equal.

A trapezium has one pair of opposite sides parallel.

Any quadrilateral is made up of two triangles. Consider the below quadrilateral.

Sum of angles of quadrilateral = $2 \times 180^{\circ} = 360^{\circ}$.

Find the angles $x$ and $y$ in the diagrams below.

Solution