Look around you and you’ll see a world filled with angles. Whether you're talking about the angle of a beam in a cross or the slope of a roof, you need tools that can measure these angles with precision. Though each profession has it own specialty tools for determining angles, some are used in multiple trades and in the classroom. When you need to measure an angle, choose the tool that fits the application.
Blueprint

Architects drafting blueprints by hand for bridges or landscape design use a variety of tools to accurately measure distances and angles. A Tsquare is used to draw horizontal lines and measure 90degree angles in relation to those lines. Use an adjustable triangle to measure angles between 0 and 90 degrees by placing it on the horizontal axis and adjusting the hinged edge till it lines up with the angled line you want to measure. If you need to copy an angle precisely, couple a compass with a ruler to measure the angle and draw an identical one.
Surveying

Surveyors use tools to measure horizontal and vertical angles in relation to the earth’s surface. A transit level has a movable telescope that is aimed at a rod to determine a horizontal level and the angle of inclination in degrees, minutes and seconds. This is useful for determining the grade of a roadway or a foundation of a home. Forestry professionals use a clinometer to calculate tree height from the angle formed between the clinometer and the tree. The handheld instrument is used by looking through the eyepiece at the highest tip of the tree and then reading the measurement on the dial. Add this to the height from the instrument to the ground and you have the total height of the tree.
Geometry

Many students are introduced to tools for measuring angles in high school geometry class. A protractor is a ruler with a semicircle attached to it. Lay its straight edge on the horizontal side of an angle and read where the hypotenuse  or angled side  crosses the protractor to determine the angle in degrees. If you have an angle that is 30, 45, 60 or 90 degrees, a set square can be laid on it to determine the degrees. The angle of the triangle is preset to 30, 60 and 90 degrees on one type, and the direction it is oriented determines the degrees of angle. A second set square is used for measuring 45 and 90 degrees.
Carpentry

Carpenters are able to build straight walls and level floors by using a bevy of tools that measure angles. A speed square is a threesided “square” with angle measurements from 0 to 60 marked on its diagonal side. Measure angles by laying it along a board's edge and reading the degrees of angle. A bevel protractor is used to measure the angle on the end of a board by rotating the adjustable arm on the protractor until it clamps down onto the wood. Simply read the degrees on the dial to know the angle the wood is cut at.
References
 TheHousePlansGuide.com: Make Your Own Blueprint
 DraftingSteals.com: Drafting TSquares
 Survey History: The Surveyor's Basic Tools
 Bob Vila: The Transit Level
 This Old House: Working the Angles
 Math Open Reference: Copying an Angle
 ELMS Environmental Education Center: How to Use a Clinometer
 Technology Student: Drawing Angles with Set Squares
 Fowler High Precision: Bevel Protractor
 Photo Credit Arman Zhenikeyev/iStock/Getty Images