Measuring Angles
Measuring angles is a fundamental geometry skill in Grade 8 math (Yoshiwara Core Math) using a protractor. A full rotation equals 360°. Angles are classified as acute (<90°), right (=90°), obtuse (90°–180°), or straight (=180°). To measure: place the protractor center at the vertex, align the baseline with one ray, read where the other ray crosses. A protractor's two scales allow measuring from either direction — always choose the scale giving a reading consistent with whether the angle is acute or obtuse. Complementary angles sum to 90°; supplementary angles sum to 180°.
Key Concepts
Property We use degrees to measure how open an angle is. The symbol for a degree is $\degree$. A right angle is $90\degree$, and a straight angle is $180\degree$. The degree measure of an acute angle is less than $90\degree$, and the degree measure of an obtuse angle is between $90\degree$ and $180\degree$. The measure of an angle does not depend on the orientation of the angle, or on how long the sides are. It only depends on how open the sides are.
Examples If two angles form a right angle ($90\degree$) and one angle is $35\degree$, the other angle must be $90\degree 35\degree = 55\degree$. An angle that measures $125\degree$ is an obtuse angle because its measure is between $90\degree$ and $180\degree$. If two angles form a straight line ($180\degree$) and one is $100\degree$, the other must be $180\degree 100\degree = 80\degree$.
Explanation Degrees are like tiny measurement units for angles. A right angle has 90 of them, and a straight line has 180. The more open the angle, the more degrees it measures, regardless of how long its sides are.
Common Questions
How do you measure an angle with a protractor?
Place the center mark on the vertex. Align the 0° baseline with one ray. Read degrees where the other ray crosses the scale.
What is the difference between acute, right, and obtuse angles?
Acute < 90°; right = 90°; obtuse is between 90° and 180°.
Why does a protractor have two scales?
To measure from either direction. Use the scale starting at 0° from the ray you aligned the baseline with.
What do complementary and supplementary angles sum to?
Complementary = 90°; supplementary = 180°.
How many degrees are in a full rotation?
360°. Half rotation = 180° (straight angle); quarter rotation = 90° (right angle).