Measurement - Measuring and Drawing Angles

An angle is formed when two rays or line segments, called arms, meet at a common endpoint called the vertex. Visually, you can imagine this as the corner of a book or the hands of a clock meeting at the center.

Angles are measured in units called degrees, represented by the symbol $^\circ$. A full circle or a complete rotation is $360^\circ$. Visually, a degree is $\frac{1}{360}$ of a full turn.

Angles are classified by their size: An Acute angle is less than $90^\circ$ (looks like a sharp 'V'); a Right angle is exactly $90^\circ$ (looks like an 'L' shape); an Obtuse angle is greater than $90^\circ$ but less than $180^\circ$ (looks like a wide open chair); a Straight angle is exactly $180^\circ$ (looks like a flat line); and a Reflex angle is greater than $180^\circ$ but less than $360^\circ$.

A protractor is the primary tool used for measuring and drawing angles. It is usually a semi-circle marked from $0^\circ$ to $180^\circ$. It has two scales: an inner scale and an outer scale. You must choose the scale that starts at $0^\circ$ on the baseline where one arm of your angle lies.

To measure an angle, place the center mark of the protractor exactly on the vertex of the angle and align the $0^\circ$ line (baseline) with one arm of the angle. Follow the scale from zero up to where the second arm crosses the edge of the protractor.

To draw an angle (e.g., $65^\circ$), first draw a straight line and mark a point as the vertex. Align your protractor's center on that vertex and the baseline on your line. Mark a dot at the $65^\circ$ mark on the correct scale, then use a ruler to connect the vertex to that dot.

Angles on a straight line always add up to $180^\circ$. If you see a straight line divided into two angles, you can find the missing one by subtracting the known angle from $180^\circ$. Visually, this looks like two adjacent angles sitting on a flat horizontal base.

Angles around a point always sum to $360^\circ$. If several angles meet at a single central point like spokes on a wheel, their combined measures will always equal a full rotation.