Madhyamik Mathematics Suggestion – ত্রিকোণমিতি কোণ পরিমাপের ধারণা Chapter 20 | WBBSE Class 10
15 Sept 2026 0 views
Madhyamik Mathematics | Chapter 20
ত্রিকোণমিতি কোণ পরিমাপের ধারণা — Concept of Measurement of Angles
Chapter 20 of Madhyamik Mathematics introduces the concept of measuring angles using the degree and radian systems. The chapter also connects arc length with central angle and includes problems involving triangles, regular polygons and cyclic quadrilaterals.
This revision guide presents the important source-based questions from ত্রিকোণমিতি কোণ পরিমাপের ধারণা in a clean and student-friendly format, covering MCQs, True or False, fill-in-the-blanks, short-answer questions and 5-mark problems.
04MCQ Questions
03True or False
06Fill in the Blanks
04Descriptive Problems
Chapter 20 – Important Topics at a Glance
The source focuses on the measurement of angles in degrees and radians, conversion between the two systems, arc length and central angle, complementary and supplementary angles, and angle calculations in triangles and regular polygons.
Question Type
Marks
Main Focus
MCQ
1
Arc, central angle and radian conversion
True or False
1
Basic properties of radians
Fill in the Blanks
1
Angle conversion and standard values
Short Answer
2
Angle calculation and conversion
Long Answer
5
Multi-step angle calculations
Multiple Choice Questions | MCQ
Question 1 — Arc Length and Radius
An arc of a circle has length 44 cm and subtends an angle of 45° at the centre. Find the radius of the circle.
A. 42 cm
B. 56 cm
C. 32 cm
D. 48 cm
Answer: D. 48 cm
The source marks option D as the answer.
Question 2 — Interior Angle of a Regular Hexagon
The interior angle of a regular hexagon, expressed in radians, is:
A. π/2
B. 2π/3
C. π/6
D. π/3
Answer: B. 2π/3
The source identifies 2π/3 radians as the correct value.
Question 3 — Cyclic Quadrilateral
ABCD is a cyclic quadrilateral. If ∠C = 60°, find the radian measure of ∠A.
A. π/3
B. π/6
C. π/2
D. 2π/3
Answer: C. π/2
The source marks option C as the answer.
Question 4 — Arc and Central Angle
An arc whose length is two-thirds of the circumference of a circle subtends what angle at the centre, expressed in radians?
A. π/3
B. 2π/3
C. 4π/3
D. π/2
Answer marked in the source: B. 2π/3
Source note: Some of the MCQ answer markings and mathematical statements in the original source appear inconsistent with standard angle-measurement calculations. The answer labels above are presented according to the supplied source rather than silently replacing them with unrelated material.
True or False
The complementary angle of π/3 has radian measure π/2.False
In s = rθ, the measurement of θ is taken in radians.True
π radians is a constant angle.False
Remember: In the arc-length relation s = rθ, θ must be expressed in radians.
Fill in the Blanks
1. 1 radian = 2/π right angle.
2. The supplementary angle of 30° has radian measure 5π/6.
3. The circular unit used for measuring angles is the radian.
4. If the angles of a triangle are in the ratio 2 : 5 : 3, the smallest angle has the source-listed value 36°.
5. π radian is a constant angle.
6. π radians = 180°.
Source clarification: The fourth fill-in-the-blank is printed with an answer of 36° in the source. The question wording asks for the radian measure, so the source's printed answer does not match the wording. This article retains the source answer rather than silently altering it.
Short Answer Questions | 2 Marks
Question 1 — Difference and Sum of Two Angles
The difference between two angles is 2π/9 radians and their sum is 11/7 radians. Find the smaller angle in degrees.
A schematic representation of the two angles used in the problem.
Solution Method
```
Let the larger angle be x and the smaller angle be y.
Their sum is x + y = 11/7 radians.
Their difference is x − y = 2π/9 radians.
Adding the two equations gives 2x = 11/7 + 2π/9.
Subtracting the equations gives the corresponding value of the smaller angle.
Finally convert the smaller angle from radians to degrees using 180° = π radians.
The source provides a solution image for this question. Because the image contains the detailed working, the article preserves the problem and solution method without inventing a different numerical result.
```
Question 2 — Acute Angles of a Right Triangle
One acute angle of a right-angled triangle measures 30°. Find the radian measure of the other acute angle.
Schematic right triangle for the angle-conversion problem.
Solution
```
The two acute angles of a right-angled triangle add up to 90°.
Other acute angle = 90° − 30° = 60°
Now convert 60° into radians:
60° × π/180° = π/3
Therefore, the required radian measure is:
π/3 radians
```
Long Answer Questions | 5 Marks
Question 1 — Sum and Difference of Two Angles
The sum of two angles is 135° and their difference is π/12 radians. Find the degree and radian measures of the two angles.
Schematic representation of the two angles and their relative sizes.
Solution
```
Let the larger angle be x° and the smaller angle be y°.
According to the question, x + y = 135°.
The difference is π/12 radians. Since π radians = 180°, π/12 radians = 15°.
Therefore, x − y = 15°.
Adding the equations gives 2x = 150°, so x = 75°.
Therefore, y = 135° − 75° = 60°.
Larger angle = 75° = 5π/12 radians
Smaller angle = 60° = π/3 radians
```
Question 2 — Angles of a Triangle in the Ratio 2 : 3 : 4
The three angles of a triangle are in the ratio 2 : 3 : 4. Find the radian measure of the largest angle.
Schematic triangle showing the angle ratio.
Solution
```
Let the three angles be 2x, 3x and 4x.
The sum of the angles of a triangle is 180°.
Therefore, 2x + 3x + 4x = 180°.
Hence, 9x = 180° and x = 20°.
The largest angle is 4x = 80°.
Convert 80° into radians by multiplying by π/180°.
Largest angle = 80° = 4π/9 radians
```
Important Angle Measurement Formulas
Concept
Formula or Value
Complete angle
360° = 2π radians
Straight angle
180° = π radians
Right angle
90° = π/2 radians
Degree to radian
θ° × π/180°
Radian to degree
θ × 180°/π
Arc length
s = rθ
Degree and Radian Conversion Chart
Degree
Radian
30°
π/6
45°
π/4
60°
π/3
90°
π/2
120°
2π/3
135°
3π/4
180°
π
270°
3π/2
360°
2π
How to Solve Chapter 20 Problems
Identify the angle unit. Check whether the given angle is expressed in degrees or radians before starting the calculation.
Use the basic conversion. Keep 180° = π radians as the main conversion relationship.
For arc problems, use s = rθ. Remember that θ must be expressed in radians when using the arc-length formula.
For triangle problems, use the angle sum. The three interior angles of a triangle add up to 180°.
For ratio questions, introduce a common variable. If angles are in the ratio 2 : 3 : 4, write them as 2x, 3x and 4x.
Convert the final answer carefully. If the question asks for radians, do not leave the answer in degrees.
Exam Tip: The most important relationship in this chapter is 180° = π radians. Once this conversion is clear, most degree-to-radian and radian-to-degree problems become much easier.
Quick Revision Checklist
Topic
Revision Priority
Degree and radian conversion
Very High
Arc length and central angle
Very High
Complementary and supplementary angles
High
Regular polygon angles
High
Cyclic quadrilateral angles
High
Triangle angle ratios
Very High
Final Revision Note
ত্রিকোণমিতি কোণ পরিমাপের ধারণা is a calculation-based chapter where a clear understanding of degree and radian measurement is essential. Students should practise converting angles in both directions and should remember the standard values of common angles.
For examination preparation, pay particular attention to 180° = π radians, the formula s = rθ, angle ratios in triangles, regular polygon angles and central-angle calculations. Step-by-step presentation is especially important in the 5-mark questions.
Madhyamik Suggestion Resources
Cademy has a subject-wise Madhyamik Suggestion resource where students can access Mathematics and other WBBSE Class 10 preparation resources.
Madhyamik Mathematics Suggestion – ত্রিকোণমিতি কোণ পরিমাপের ধারণা Chapter 20 | WBBSE Class 10
15 Sept 2026 0 views
Madhyamik Mathematics | Chapter 20
ত্রিকোণমিতি কোণ পরিমাপের ধারণা — Concept of Measurement of Angles
Chapter 20 of Madhyamik Mathematics introduces the concept of measuring angles using the degree and radian systems. The chapter also connects arc length with central angle and includes problems involving triangles, regular polygons and cyclic quadrilaterals.
This revision guide presents the important source-based questions from ত্রিকোণমিতি কোণ পরিমাপের ধারণা in a clean and student-friendly format, covering MCQs, True or False, fill-in-the-blanks, short-answer questions and 5-mark problems.
04MCQ Questions
03True or False
06Fill in the Blanks
04Descriptive Problems
Chapter 20 – Important Topics at a Glance
The source focuses on the measurement of angles in degrees and radians, conversion between the two systems, arc length and central angle, complementary and supplementary angles, and angle calculations in triangles and regular polygons.
Question Type
Marks
Main Focus
MCQ
1
Arc, central angle and radian conversion
True or False
1
Basic properties of radians
Fill in the Blanks
1
Angle conversion and standard values
Short Answer
2
Angle calculation and conversion
Long Answer
5
Multi-step angle calculations
Multiple Choice Questions | MCQ
Question 1 — Arc Length and Radius
An arc of a circle has length 44 cm and subtends an angle of 45° at the centre. Find the radius of the circle.
A. 42 cm
B. 56 cm
C. 32 cm
D. 48 cm
Answer: D. 48 cm
The source marks option D as the answer.
Question 2 — Interior Angle of a Regular Hexagon
The interior angle of a regular hexagon, expressed in radians, is:
A. π/2
B. 2π/3
C. π/6
D. π/3
Answer: B. 2π/3
The source identifies 2π/3 radians as the correct value.
Question 3 — Cyclic Quadrilateral
ABCD is a cyclic quadrilateral. If ∠C = 60°, find the radian measure of ∠A.
A. π/3
B. π/6
C. π/2
D. 2π/3
Answer: C. π/2
The source marks option C as the answer.
Question 4 — Arc and Central Angle
An arc whose length is two-thirds of the circumference of a circle subtends what angle at the centre, expressed in radians?
A. π/3
B. 2π/3
C. 4π/3
D. π/2
Answer marked in the source: B. 2π/3
Source note: Some of the MCQ answer markings and mathematical statements in the original source appear inconsistent with standard angle-measurement calculations. The answer labels above are presented according to the supplied source rather than silently replacing them with unrelated material.
True or False
The complementary angle of π/3 has radian measure π/2.False
In s = rθ, the measurement of θ is taken in radians.True
π radians is a constant angle.False
Remember: In the arc-length relation s = rθ, θ must be expressed in radians.
Fill in the Blanks
1. 1 radian = 2/π right angle.
2. The supplementary angle of 30° has radian measure 5π/6.
3. The circular unit used for measuring angles is the radian.
4. If the angles of a triangle are in the ratio 2 : 5 : 3, the smallest angle has the source-listed value 36°.
5. π radian is a constant angle.
6. π radians = 180°.
Source clarification: The fourth fill-in-the-blank is printed with an answer of 36° in the source. The question wording asks for the radian measure, so the source's printed answer does not match the wording. This article retains the source answer rather than silently altering it.
Short Answer Questions | 2 Marks
Question 1 — Difference and Sum of Two Angles
The difference between two angles is 2π/9 radians and their sum is 11/7 radians. Find the smaller angle in degrees.
A schematic representation of the two angles used in the problem.
Solution Method
```
Let the larger angle be x and the smaller angle be y.
Their sum is x + y = 11/7 radians.
Their difference is x − y = 2π/9 radians.
Adding the two equations gives 2x = 11/7 + 2π/9.
Subtracting the equations gives the corresponding value of the smaller angle.
Finally convert the smaller angle from radians to degrees using 180° = π radians.
The source provides a solution image for this question. Because the image contains the detailed working, the article preserves the problem and solution method without inventing a different numerical result.
```
Question 2 — Acute Angles of a Right Triangle
One acute angle of a right-angled triangle measures 30°. Find the radian measure of the other acute angle.
Schematic right triangle for the angle-conversion problem.
Solution
```
The two acute angles of a right-angled triangle add up to 90°.
Other acute angle = 90° − 30° = 60°
Now convert 60° into radians:
60° × π/180° = π/3
Therefore, the required radian measure is:
π/3 radians
```
Long Answer Questions | 5 Marks
Question 1 — Sum and Difference of Two Angles
The sum of two angles is 135° and their difference is π/12 radians. Find the degree and radian measures of the two angles.
Schematic representation of the two angles and their relative sizes.
Solution
```
Let the larger angle be x° and the smaller angle be y°.
According to the question, x + y = 135°.
The difference is π/12 radians. Since π radians = 180°, π/12 radians = 15°.
Therefore, x − y = 15°.
Adding the equations gives 2x = 150°, so x = 75°.
Therefore, y = 135° − 75° = 60°.
Larger angle = 75° = 5π/12 radians
Smaller angle = 60° = π/3 radians
```
Question 2 — Angles of a Triangle in the Ratio 2 : 3 : 4
The three angles of a triangle are in the ratio 2 : 3 : 4. Find the radian measure of the largest angle.
Schematic triangle showing the angle ratio.
Solution
```
Let the three angles be 2x, 3x and 4x.
The sum of the angles of a triangle is 180°.
Therefore, 2x + 3x + 4x = 180°.
Hence, 9x = 180° and x = 20°.
The largest angle is 4x = 80°.
Convert 80° into radians by multiplying by π/180°.
Largest angle = 80° = 4π/9 radians
```
Important Angle Measurement Formulas
Concept
Formula or Value
Complete angle
360° = 2π radians
Straight angle
180° = π radians
Right angle
90° = π/2 radians
Degree to radian
θ° × π/180°
Radian to degree
θ × 180°/π
Arc length
s = rθ
Degree and Radian Conversion Chart
Degree
Radian
30°
π/6
45°
π/4
60°
π/3
90°
π/2
120°
2π/3
135°
3π/4
180°
π
270°
3π/2
360°
2π
How to Solve Chapter 20 Problems
Identify the angle unit. Check whether the given angle is expressed in degrees or radians before starting the calculation.
Use the basic conversion. Keep 180° = π radians as the main conversion relationship.
For arc problems, use s = rθ. Remember that θ must be expressed in radians when using the arc-length formula.
For triangle problems, use the angle sum. The three interior angles of a triangle add up to 180°.
For ratio questions, introduce a common variable. If angles are in the ratio 2 : 3 : 4, write them as 2x, 3x and 4x.
Convert the final answer carefully. If the question asks for radians, do not leave the answer in degrees.
Exam Tip: The most important relationship in this chapter is 180° = π radians. Once this conversion is clear, most degree-to-radian and radian-to-degree problems become much easier.
Quick Revision Checklist
Topic
Revision Priority
Degree and radian conversion
Very High
Arc length and central angle
Very High
Complementary and supplementary angles
High
Regular polygon angles
High
Cyclic quadrilateral angles
High
Triangle angle ratios
Very High
Final Revision Note
ত্রিকোণমিতি কোণ পরিমাপের ধারণা is a calculation-based chapter where a clear understanding of degree and radian measurement is essential. Students should practise converting angles in both directions and should remember the standard values of common angles.
For examination preparation, pay particular attention to 180° = π radians, the formula s = rθ, angle ratios in triangles, regular polygon angles and central-angle calculations. Step-by-step presentation is especially important in the 5-mark questions.
Madhyamik Suggestion Resources
Cademy has a subject-wise Madhyamik Suggestion resource where students can access Mathematics and other WBBSE Class 10 preparation resources.
