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Sexagesimal Measure
Everyday angles in this book use the sexagesimal English degrees system. One full turn is 360 deg. Each degree splits into 60 minutes, and each minute splits into 60 seconds, so 1 deg = 60 min = 3600 sec. A right angle is 90 deg, a straight angle is 180 deg, and a full turn is 360 deg. Centesimal measure (grades) exists in some older books but is beyond this book. Circular measure uses radians and
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Sexagesimal Measure
What is it?
Everyday angles in this book use the sexagesimal English degrees system. One full turn is 360 deg. Each degree splits into 60 minutes, and each minute splits into 60 seconds, so 1 deg = 60 min = 3600 sec. A right angle is 90 deg, a straight angle is 180 deg, and a full turn is 360 deg. Centesimal measure (grades) exists in some older books but is beyond this book. Circular measure uses radians and is the other system you must convert.
In simple words
- Everyday angles in this book use the sexagesimal English degrees system.
- In English degrees, 1 deg = 60 min and 1 min = 60 sec, so 1 deg = 3600 sec.
- Centesimal measure divides a right angle into 100 grades.
- Write 40 deg 20 min, not a mix of grades.
Important terms
sexagesimal: Everyday angles in this book use the sexagesimal English degrees system.
English degrees: Everyday angles in this book use the sexagesimal English degrees system.
1 deg = 60 min = 3600 sec: Each degree splits into 60 minutes, and each minute splits into 60 seconds, so 1 deg = 60 min = 3600 sec.
Centesimal: Centesimal measure (grades) exists in some older books but is beyond this book.
What you should learn
- Explain sexagesimal measure in clear mathematical language
- Apply the ideas in degrees minutes seconds
- Solve problems involving other systems
Examples
- 90 deg is a right angle
- 30 min is half of 1 deg
- 1 deg 30 min = 1.5 deg
DEGREES MINUTES SECONDS
In English degrees, 1 deg = 60 min and 1 min = 60 sec, so 1 deg = 3600 sec. A half degree is 30 min. When you add angles, 60 min become 1 deg, just as 60 seconds become 1 minute on a clock. Keep the three units lined up when you add or subtract.
OTHER SYSTEMS
Centesimal measure divides a right angle into 100 grades. The course tells you it is beyond this book, so do not mix grades with degrees in an exam answer. Circular measure uses radians: the angle is the arc length divided by the radius. You will need both degrees and radians, and the link between them, on the next page.
Recommended for Class 9
Full school-level explanation
Everyday angles in this book use the sexagesimal English degrees system. One full turn is 360 deg. Each degree splits into 60 minutes, and each minute splits into 60 seconds, so 1 deg = 60 min = 3600 sec. A right angle is 90 deg, a straight angle is 180 deg, and a full turn is 360 deg. Centesimal measure (grades) exists in some older books but is beyond this book. Circular measure uses radians and is the other system you must convert.
Degrees for drawing; radians for the circle:
What it means
Everyday angles in this book use the sexagesimal English degrees system.
Main ideas
1. DEGREES MINUTES SECONDS: In English degrees, 1 deg = 60 min and 1 min = 60 sec, so 1 deg = 3600 sec. 2. OTHER SYSTEMS: Centesimal measure divides a right angle into 100 grades.
Why it matters
Write 40 deg 20 min, not a mix of grades. If a calculator is in radian mode, a 90 deg sine will look wrong. Sexagesimal means base 60, which is why minutes and seconds come in sixties.
How to answer in an exam
Do not invent a centesimal working in this chapter. Stick to English degrees and, when asked, radians. Remember 1 deg = 60 min = 3600 sec so you can convert a decimal degree into minutes.
DEGREES MINUTES SECONDS
In English degrees, 1 deg = 60 min and 1 min = 60 sec, so 1 deg = 3600 sec. A half degree is 30 min. When you add angles, 60 min become 1 deg, just as 60 seconds become 1 minute on a clock. Keep the three units lined up when you add or subtract.
Remember
- 1 deg = 60 min
- 1 deg = 3600 sec
- 60 min become 1 deg
Examples
- 90 deg is a right angle
- 30 min is half of 1 deg
- 1 deg 30 min = 1.5 deg
OTHER SYSTEMS
Centesimal measure divides a right angle into 100 grades. The course tells you it is beyond this book, so do not mix grades with degrees in an exam answer. Circular measure uses radians: the angle is the arc length divided by the radius. You will need both degrees and radians, and the link between them, on the next page.
Remember
- Centesimal
- beyond this book
- Circular
- radians
Examples
- Degrees: 90, 180, 360
- Centesimal: mentioned, not used here
- Circular: radians on a circle
Remember
- sexagesimal
- English degrees
- 1 deg = 60 min = 3600 sec
- Centesimal
- beyond this book
- radians
- Sexagesimal
- base 60
How the ideas connect
Write 40 deg 20 min, not a mix of grades. If a calculator is in radian mode, a 90 deg sine will look wrong. Sexagesimal means base 60, which is why minutes and seconds come in sixties.
Deeper understanding
Go beyond memorising Sexagesimal Measure. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Write 40 deg 20 min, not a mix of grades. If a calculator is in radian mode, a 90 deg sine will look wrong. Sexagesimal means base 60, which is why minutes and seconds come in sixties.
Common mistakes
Exam focus
Core Idea
Key Terms
Main Pattern
Worked Reminder
Exam focus
Quick revision
- sexagesimal
- English degrees
- 1 deg = 60 min = 3600 sec
- Centesimal
- sexagesimal: Everyday angles in this book use the sexagesimal English degrees system.
- English degrees: Everyday angles in this book use the sexagesimal English degrees system.
Do not invent a centesimal working in this chapter. Stick to English degrees and, when asked, radians. Remember 1 deg = 60 min = 3600 sec so you can convert a decimal degree into minutes.
For long answers on Sexagesimal Measure: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- sexagesimal
- English degrees
- 1 deg = 60 min = 3600 sec
- Centesimal
Important formulas
- sexagesimal
- English degrees
- 1 deg = 60 min = 3600 sec
Common exam traps
- Do not invent a centesimal working in this chapter.
- Stick to English degrees and, when asked, radians.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not invent a centesimal working in this chapter.
- Mistake
Stick to English degrees and, when asked, radians.
- Mistake
Do not mix up degrees minutes seconds with other systems; use the condition given in the question.
- Mistake
Do not invent a centesimal working in this chapter. Stick to English degrees and, when asked, radians. Remember 1 deg = 60 min = 3600 sec so you can convert a d
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
sexagesimal
English degrees
1 deg = 60 min = 3600 sec
Centesimal
Everyday angles in this book use the sexagesimal English degrees system. One full turn is 360 deg. Each degree splits into 60 minutes, and each minute splits in
1 deg = 60 min = 3600 sec
- Definition
- Everyday angles in this book use the sexagesimal English degrees system. One full turn is 360 deg. Each degree splits into 60 minutes, and each minute splits in
- Formula
- 1 deg = 60 min = 3600 sec
- Example
- 90 deg is a right angle
- Critical warning
- Do not invent a centesimal working in this chapter.
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Exam Practice
Define
Q1. Define Sexagesimal Measure.
Explain
Q2. Explain: DEGREES MINUTES SECONDS.
Example
Q3. Give one clear example of Sexagesimal Measure and say why it fits.
Mistake
Q4. State one common mistake students make about Sexagesimal Measure.
Exam note
Q5. Write a short exam note on Sexagesimal Measure: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.