Geometry

 Names for Angles
 
 * **Acute angles**. An angle of less than 90 degrees is called an acute angle. Angle a is acute.
 * **Right angle**. An angle of exactly 90 degrees is called a right angle. We mark then with a small square. Angle b is a right angle.
 * **Obtuse angle**. An angle greater than 90 degrees and less than 180 degrees is called an obtuse angle. Angle c is obtuse.
 * **Reflex angle**. An angle greater than 180 degrees is called a reflex angle. Angle d is reflex.

 Supplementary Angles
Any two angles that add up to 180 degrees are known as supplementary angles. 

 Angles on a Straight Line
Angles on a straight line add up to 180 degrees.  

 Angles at a Point
The angles at a point add up to 360 degrees.  

 Parallel line angles
Lines AB and CD are parallel to one another. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;"> 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 16px;"> Vertically Opposite Angles
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">Vertically opposite angles are always equal. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">In the main diagram, angles a and d are vertically opposite. So are angles b and c, angles e and h and angles f and g. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;"> 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 16px;"> Corresponding Angles
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">Corresponding angles are always equal. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">In the main diagram, angles b and f are corresponding angles. So are angles a and e, angles c and g and angles d and h. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">Corresponding angles are also sometimes called 'F-angles' because of the F-shape they make. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;"> 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 16px;"> Alternate Angles
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">Alternate angles are always equal. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">In the main diagram, angles d and e are alternate angles. So are angles c and f. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">Alternate angles are sometimes called 'Z-angles' because of the Z-shape they make. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;"> 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 16px;"> Adjacent Angles
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">Adjacent angles always add up to 180 degrees. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">In the diagram angle a and b are adjacent angles. There are lots of pairs of adjacent angles (a and c, b and d, c and d, e and g, e and f, f and h, g and h are all adjacent angles). <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">Adjacent angles are situated next to each other. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;"> 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 16px;"> Interior or Allied Angles
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">Interior angles (also called allied or inner angles) always add up to 180 degrees. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">In the main diagram, angles c and e are interior angles. So are angles d and f. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">Interior angles are sometimes called 'C-angles' or 'U-angles' because of the u or c shape they make. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;"> 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 18px;"> Angles in polygons
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">A polygon is a many sided shape the simplest being a triangle with just three sides. A polygon has interior angles which are angles inside the shape and exterior angles which are angles created outside the shape by extending their sides (see the diagram below). 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 16px;"> Interior Angles in Triangles
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">The interior angles in a triangle add up to 180 degrees. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;"> 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 16px;"> Interior Angles in Quadrilaterals
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">The angles in a quadrilateral add up to 360 degrees. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;"> 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 16px;"> Interior angles in any polygon
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">The interior angles in an n-sided polygon will add up to 180(n - 2) degrees. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">For example, the pentagon below the interior angles will add up to 180(5 - 2) = 180 x 3 = 540 degrees. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;"> <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">In regular polygon (where all the sides are of equal length), all the interior angles are equal. We can find an interior angle of a regular polygon by finding the total they all add up to using the above method and then dividing that total by the number of sides. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">For example, the interior angles in a regular pentagon will add up to 540 degrees. There are 5 sides to a pentagon. Therefore, one interior angle is 540 divided by 5, which gives 108 degrees. 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 16px;"> Exterior angles in any polygon
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">The exterior angles of any polygon add up to 360 degrees. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">The diagram shows the exterior angles of a pentagon, which will add up to 360 degrees. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;"> <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">In a regular polygon, all exterior angles are equal. <span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">For example one exterior angle of a regular pentagon is 360 divided by 5, which gives 72 degrees. 

<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 16px;"> The Interior And Exterior Angle At Any Corner
<span style="background-color: #ffffff; color: #444444; font-family: verdana,arial,geneva,lucida,sans-serif; font-size: 12px;">At any corner of a polygon, the interior and exterior angles are supplementary. That is, they add up to 180 degrees.