What Is an Angle?
Aligned to 4.MD.C.5 — Common Core State Standards for Mathematics.
What this lesson teaches
An angle is formed by two rays that start from the same point, called the vertex. Angle size is how far one ray is turned from the other, measured in degrees. A full turn around a circle is 360 degrees.
Worked examples
Example 1
Imagine a clock hand turning all the way around: that full circle is 360 degrees. If a ray turns one quarter of the way around the circle, that is one fourth of 360: 360 / 4 = 90 degrees. So a quarter turn makes a 90 degree angle.
Example 2
Half a turn is half of 360: 360 ÷ 2 = 180 degrees. That is why a straight line measures 180.
Example 3
An angle's size does not depend on how long you draw its rays. A 30-degree angle with short arms and one with long arms are the same angle.
Practice questions
- How many degrees is a half turn around a circle?
- A ray turns one third of the way around a circle. How many degrees is that?
- An angle is 1/6 of a full circle. How many degrees does it measure?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
¿Qué es un ángulo?
Un ángulo se forma con dos rayos que salen del mismo punto, llamado vértice. El tamaño del ángulo es cuánto gira un rayo respecto al otro, medido en grados. Una vuelta completa alrededor de un círculo es 360 grados.
Ejemplo 1: Imagina la manecilla de un reloj girando por completo: ese círculo completo es 360 grados. Si un rayo gira un cuarto de la vuelta alrededor del círculo, eso es un cuarto de 360: 360 / 4 = 90 grados. Entonces un cuarto de vuelta forma un ángulo de 90 grados.
Ejemplo 2: Media vuelta es la mitad de 360: 360 ÷ 2 = 180 grados. Por eso una línea recta mide 180.
Ejemplo 3: El tamaño de un ángulo no depende de qué tan largos dibujes sus rayos. Un ángulo de 30 grados con brazos cortos y otro con brazos largos son el mismo ángulo.
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