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180 Degree Angle: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">180 Degree Angle180 Degree Angle: Definition and ExamplesTable of Contents180 Degree Angle: Definition, Construction, and Examples Definition of 180 Degree Angle

A 180 degree angle is an angle that forms a straight line. It is created when the two arms of the angle extend in opposite directions from a common point, forming opposite rays. Because of its straight-line appearance, the 180 degree angle is also commonly referred to as a "straight angle" or "flat angle". In terms of radians, a 180 degree angle equals π\piπ radians, which is approximately 3.14 radians.

The 180 degree angle has important relationships with other angle types. Half of a 180° angle measures 90°, which is a right angle. Twice the 180° angle measures 360°, known as a complete angle or full angle. Angles between 90° and 180° are called obtuse angles, while angles greater than 180° and less than 360° are called reflex angles. Two angles that add up to 180 degrees are called supplementary angles, and angles in a linear pair always add up to 180 degrees.

Examples of 180 Degree Angle Example 1: Finding a Missing Angle in a Straight Line Problem:

What is the measure of the angle BOC?

180 degree angle

Step-by-step solution:

Step 1, Remember that a straight angle measures 180 degrees. When two angles form a straight line, they add up to 180 degrees.

Step 2, Look at what we know. Angle AOB measures 40°.

Step 3, Set up an equation to find the unknown angle BOC (let's call it x).

x + 40° = 180°

Step 4, Solve for x by subtracting 40° from both sides.

x = 180° - 40°

x = 140°

Step 5, Therefore, angle BOC measures 140°.

Example 2: Understanding Relationships Between Different Angle Types Problem:

How is a 180 degree angle related to a complete angle and a right angle?

Step-by-step solution:

Step 1, Understand what a complete angle is. A complete angle measures 360 degrees, which is a full circle.

Step 2, Find the relationship between a complete angle and a 180 degree angle. Half of the complete circle angle is 180 degree angle. So, a 180° angle is exactly half of a complete angle.

Step 3, Understand what a right angle is. A right angle measures 90 degrees.

Step 4, Find the relationship between a right angle and a 180 degree angle. Twice the right angle equals a straight angle. This means two adjacent right angles form a straight angle of 180°.

180 degree angle

Example 3: Angles on a Clock Face Problem:

What is the angle made by the hour hand and the minute hand when the clock reads 06:00?

Step-by-step solution:

Step 1, Visualize the position of both hands on the clock at 6:00. The hour hand points to 6, which is at the bottom of the clock. The minute hand points to 12, which is at the top of the clock.

Step 2, Determine how many degrees separate the two hands. The hour hand at 6 is at the 180° position from the 12 o'clock position. The minute hand at 12 is at the 0° or 360° position.

Step 3, Calculate the angle between the two hands. Since the hands are pointing in exactly opposite directions, they form a straight line through the center of the clock, creating a 180° angle.

Step 4, Therefore, at 6:00, the hour and minute hands form a 180° angle.

180 degree angle

Comments(3)AAdvertiserTobyNovember 4, 2025This clear def of 180 degree angle really helped my students grasp the concept! Great for making straight-line lessons click.

SSwimmerEvanNovember 4, 2025This definition really helped my students grasp 180-degree angles! It's clear and the examples made it easy for them to understand.

BBookLover25September 17, 2025I used the 180 Degree Angle definition from this page to help my kids understand straight angles during homework. The examples made it super easy to explain, and they actually got it! Thanks for breaking it down so well!

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