How to Calculate All Angles Between 0° and 180° - Comprehensive Guide

Being able to accurately calculate angles is a key skill to have in various fields, such as architecture, engineering and mechanics. Knowing how to calculate angles between 0° and 180° accurately can help you be more precise in your calculations and enable you to design and construct more complex projects.

This document describes how to calculate all angles between 0° and 180°.

What Is an Angle?

An angle is the opening between two lines that radiate from a common point. Angles are measured in degrees. A full circle has 360 degrees, so an angle of 90 degrees is one quarter of a circle.

Degree Measurement

The degree measurement used in geometry is expressed as the number of degrees, minutes, and seconds that make up the angle. To calculate an angle from 0° to 180°, use the following equation:

Angle (°) = Degrees + (Minutes/60) + (Seconds/3600)

Therefore, for example, an angle of 120°30'12'' can be expressed as 120 + (30/60) + (12/3600) which simplifies to 120.5033.

Steps to Calculate All Angles Between 0° and 180°

In order to calculate all angles between 0° and 180°, use the following steps:

1. Determine the degree measurement of the angle by using the equation above.
2. For angles between 0° and 90°, compare the degrees of the angle to the arc of a semicircle and calculate the arc, or degrees, of that portion.
3. To calculate angles between 90° and 180°, subtract the angle in degrees from 180 to get the measurement of the arc.

For example, a 120° angle is equal to the arc of a semicircle divided in two, so 120° is also equal to 60° of an arc. Therefore, the angle is 60% of a semicircle.

FAQ

What Is an Angle?

An angle is the opening between two lines that radiate from a common point. Angles are measured in degrees, so a full circle has 360 degrees.

How to Calculate an Angle?

To calculate an angle, use the equation Angle (°) = Degrees + (Minutes/60) + (Seconds/3600).

How to Calculate All Angles Between 0° and 180°?

In order to calculate all angles between 0° and 180°, determine the degree measurement of the angle by using the equation above, then for angles between 0° and 90°, compare the degrees of the angle to the arc of a semicircle and calculate the arc, or degrees, of that portion. To calculate angles between 90° and 180°, subtract the angle in degrees from 180 to get the measurement of the arc.

What Are Degrees in a Full Circle?

A full circle has 360 degrees.

How to Find the Arc of a Semicircle?

To find the arc of a semicircle, divide the angle in degrees by two.