Angle and Shapes

Understanding Angles and Shapes

Basic Concepts

Angles measure the amount of rotation between two lines that meet at a point.
Angles are usually measured in degrees. A full circle has 360 degrees.
A line that splits an angle in half, creating two equal angles, is known as an angle bisector.
Complementary angles add up to 90 degrees, supplementary angles add up to 180 degrees and angles at a point add up to 360 degrees.

Types of Angles

An angle less than 90 degrees is known as an acute angle.
An angle of exactly 90 degrees is a right angle.
An angle between 90 and 180 degrees is an obtuse angle.
An angle of exactly 180 degrees is known as a straight angle, it looks like a straight line.
An angle greater than 180 degrees but less than 360 degrees is a reflex angle.
An angle that is exactly 360 degrees is a complete angle.

Shapes and their Angles

A triangle has three angles. The sum of these angles is always 180 degrees.
A quadrilateral has four angles. The sum of the angles in a quadrilateral is 360 degrees.
The sum of interior angles in any polygon can be calculated using the formula (n-2)data, where n is the number of sides in the polygon.

Angles and Parallel Lines

When two parallel lines are crossed by a third line (a transversal), several pairs of equal (corresponding and alternate) angles are formed.
Corresponding angles are sometimes referred to as ‘F’ angles due to the shape formed by the intersecting lines. They are located in the same relative positions on the parallel lines and are equal.
Alternate angles are located between the parallel lines but on opposite sides of the transversal. They are also equal.

Applications of Angles

Angles have numerous applications in daily life, from the design of ramps and staircases, to the focusing of camera lenses, to the navigation of ships and aircraft.

Summing up Angles and Shapes

Understanding angles and shapes is critical for many areas of study, including physics, architecture, design and computing. It’s also practical for everyday problem solving. Keep practicing the key concepts and applying them to different shapes to hone your skills.