Angles and Measurement
An angle is formed by two rays sharing an endpoint.
About this topic
An angle is formed by two rays sharing an endpoint called the vertex, and it measures the amount of turn between them in degrees. Acute angles are under 90°, right angles are exactly 90°, obtuse are between 90° and 180°, a straight angle is 180° and a full turn is 360°.
A protractor measures angles. Angle names use three letters with the vertex in the middle, such as ∠ABC. Angles are central to design, navigation, architecture and trigonometry.
Worked example: if angle ABC measures 35°, it is acute; its complement is 55° and its supplement is 145°. Two angles in a figure are 3x and 2x + 10 and together form a right angle, so 5x + 10 = 90 and x = 16. A clock at 3 o'clock shows 90°, and at 4 o'clock the hands are 120° apart, because each hour is 30°.
Surveyors, pilots and carpenters measure angles constantly, for roof pitch, compass headings and mitre cuts. When using a protractor, line up the vertex and one ray with the zero line and read the correct scale, inner or outer, by checking whether the angle is acute or obtuse. A typical mistake is to read 130° when the angle clearly looks acute, which should be 50°. Estimate first and then measure to catch such slips. Also remember that the size of an angle does not depend on the length of its rays.
Key ideas
- Measured in degrees with a protractor
- Acute under 90°, right 90°, obtuse over 90°
- A straight angle is 180°
Quick check
Use cases: where Angles and Measurement helps
- Homework: review the key idea behind Angles and Measurement before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Angles and Measurement without notes.
- Visual learning: play with the interactive lab to see how Angles and Measurement changes when you adjust its inputs.
- Teaching a friend: explain Angles and Measurement in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Angles and Measurement?
An angle is formed by two rays sharing an endpoint.
What will I learn in Angles and Measurement?
Measured in degrees with a protractor. Acute under 90°, right 90°, obtuse over 90°. A straight angle is 180°.
Is Angles and Measurement part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Angles and Measurement lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Angles and Measurement?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.