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An angle is made from two rays that start from the same point. That shared starting point is called the vertex. Here is a clock at 3 o'clock.
Both hands start from one shared point in the middle. What is that point called?
What Is an Angle?
Understand that an angle is a geometric shape formed by two rays sharing a common endpoint (vertex); recognise angles in real-life contexts and 2-D shapes
What a learner can do afterwards
- Identify the vertex and arms of an angle in a diagram
- Find examples of angles in the classroom (e.g. open door, clock hands)
- Explain why two rays meeting at a point form an angle
1 · Read
An angle is made from two rays. A ray is a straight path with one endpoint that goes on forever in one direction. Both rays of an angle start from the exact same point, called the vertex. Each ray is called an arm. An ideal ray is infinite; a clock hand or a polygon side is a finite portion that stands for the ray's direction.
Try it together
A clock's hands start at the center. That center is the vertex. The hands are finite, but they stand for the directions of two rays. At 3 o'clock the hands make a square corner. We select the smaller opening between the two directions. That smaller opening is the angle we name.
Try it together
A polygon is a flat closed shape with straight sides. Two sides meet at each corner, and that corner is a vertex. A triangle has 3 vertices, a square or rectangle has 4, and a pentagon has 5. Every corner of a square or rectangle is a right angle. To compare two shapes, pair one corner from each shape and count the leftovers.
The test for an angle is strict: you need two arms meeting at one shared vertex. Two lines that never touch make no angle, however close they run. A single smooth curve has no arms and no vertex. Check the meeting point first, then look at the opening.
An acute angle has a positive opening smaller than a right angle. A right angle is a square corner, a quarter turn. An obtuse angle is greater than a right angle and less than a half turn. A half turn is straight. On a clock, the smaller opening at 1 o'clock is acute, at 3 o'clock is right, at 4 or 5 o'clock is obtuse, and at 6 o'clock the two openings are equal halves.
A door swings on its hinge. In a top view, the hinge is a point, the closed door is one direction, and the open door is another. The selected angle is the amount the door has turned from closed. A positive turn below a right angle is acute. A turn between a right angle and a half turn is obtuse. The door's fixed length does not set the opening.
An angle is two rays sharing one vertex. Each ray is an arm. Name the opening by comparing it with a right angle and a half turn.
Ten fresh original tasks (x1-x10) and two fresh original readings (reading1, reading2) authored for this topic. One Khan Academy article retained and adapted: Parallel and perpendicular lines review (academy:article:4th-engage-ny:xcfd7ce79). Two Khan Academy videos retained: Recognizing angles (academy:video:4th-engage-ny:x1781a3d6) and Drawing acute, right and obtuse angles (academy:video:4th-engage-ny:x93c8f042). All corpus licenses are null and unverified.
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