It can be a little confusing trying to understand angles, especially when you’re first starting out in geometry. But don’t worry, we’re here to help!
In geometry, an angle is defined as the figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. The rays are always straight lines. Angles can be measured in degrees, with 360 degrees making a full circle.
However, some angles can be a little tricky to measure. For example, an angle that isn’t straight across from one side to another is called an obtuse angle. This can be a little confusing for beginners, because there’s no set number of degrees for an obtuse angle – it just means that it’s not a right angle.
But don’t worry, with a little practice you’ll be able to measure any angle you come across!
The Angle:
An angle is a figure formed by two rays, or line segments, that have a common endpoint. The rays are called the sides of the angle and the endpoint is called the vertex. The measure of an angle is the angle’s size, or how far it extends from the vertex.
Degrees and Radians:
An angle can be measured in degrees or in radians. A degree is a unit of measurement that is used to measure angles in geometry. There are 360 degrees in a circle. A radian is a unit of measurement that is used to measure angles in mathematics. There are 2π radians in a circle.
The Slope of a Line:
The slope of a line is a number that describes how steep the line is. The slope can be positive or negative. A positive slope means that the line goes up as it goes to the right. A negative slope means that the line goes down as it goes to the right.
Positive and Negative Angles:
A positive angle is an angle that measures more than 0 degrees but less than 90 degrees. A negative angle is an angle that measures less than 0 degrees but more than -90 degrees.
Quadrants:
An angle is said to be in Quadrant I if it measures 0 to 90 degrees. An angle is said to be in Quadrant II if it measures 90 to 180 degrees. An angle is said to be in Quadrant III if it measures 180 to 270 degrees. An angle is said to be in Quadrant IV if it measures 270 to 360 degrees.
Angles in Triangles:
When an angle is in a triangle, it is always measured in radians. The measure of an angle in a triangle is always the sum of the measures of the other two angles in the triangle.
