Welcome To My School Study
Practice Class 8 Maths Chapter 4 Practical Geometry MCQ Questions with Answers and Solutions based on NCERT concepts. Solve fresh questions on quadrilateral construction, diagonals, angles, sides, and geometrical measurements.
Do You Know
Chapter Information
Subject: Mathematics
Class: 8
Chapter: Practical Geometry
Question Type: Multiple Choice Questions (MCQs)
Practice Set: 4
Difficulty Level: Moderate
Based On: NCERT Mathematics
Introduction
In practical geometry, students learn how to construct geometrical figures when sufficient information about their sides, angles, or diagonals is provided.
For a quadrilateral, the construction method depends on the measurements given in the question. Students must carefully identify these measurements and use the appropriate geometrical instruments.
This Practice Set 4 contains 5 fresh MCQs covering construction conditions, angle relationships, diagonals, and measurement accuracy.
What You Will Learn
✔ Understanding given measurements
✔ Identifying opposite and adjacent angles
✔ Using diagonals in constructions
✔ Understanding angle sums in quadrilaterals
✔ Applying construction principles
✔ Checking measurements during construction
Why This Topic Is Important
Practical Geometry connects theoretical geometry with actual construction. It teaches students how measurements determine the shape and structure of a geometrical figure.
Understanding these concepts helps students solve both construction-based and conceptual questions in examinations.
Exam Relevance
These questions are useful for:
✔ CBSE School Exams
✔ NCERT-Based Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Mathematics Revision
✔ Geometry Practice
Q1. What is the sum of the four interior angles of a quadrilateral?
A) $$180^\circ$$
B) $$270^\circ$$
C) $$360^\circ$$
D) $$450^\circ$$
Answer:
C) $$360^\circ$$
Useful Concept
The sum of the interior angles of every quadrilateral is:
$$360^\circ$$
Solution
A diagonal can divide a quadrilateral into two triangles.
The sum of the angles of one triangle is:
$$180^\circ$$
Therefore, the sum of the angles of two triangles is:
$$180^\circ+180^\circ=360^\circ$$
Hence, the sum of the four interior angles of a quadrilateral is:
$$360^\circ$$
Therefore, the correct answer is:
C) $$360^\circ$$
Q2. If three angles of a quadrilateral are $$80^\circ$$, $$95^\circ$$ and $$105^\circ$$, what is the fourth angle?
A) $$70^\circ$$
B) $$80^\circ$$
C) $$90^\circ$$
D) $$100^\circ$$
Answer:
B) $$80^\circ$$
Useful Concept
The sum of the four interior angles of a quadrilateral is:
$$360^\circ$$
Solution
The three given angles are:
$$80^\circ,\ 95^\circ,\ 105^\circ$$
Their sum is:
$$80^\circ+95^\circ+105^\circ=280^\circ$$
Let the fourth angle be:
$$x$$
Then:
$$280^\circ+x=360^\circ$$
Therefore:
$$x=360^\circ-280^\circ$$
$$x=80^\circ$$
Hence, the correct answer is:
B) $$80^\circ$$
Q3. In quadrilateral ABCD, which pair represents opposite angles?
A) $$\angle A$$ and $$\angle B$$
B) $$\angle B$$ and $$\angle C$$
C) $$\angle A$$ and $$\angle C$$
D) $$\angle C$$ and $$\angle D$$
Answer:
C) $$\angle A$$ and $$\angle C$$
Useful Concept
Opposite angles of a quadrilateral do not have a common side.
Solution
Consider quadrilateral:
$$ABCD$$
Its angles are:
$$\angle A,\ \angle B,\ \angle C,\ \angle D$$
The opposite angle pairs are:
$$\angle A \text{ and } \angle C$$
and:
$$\angle B \text{ and } \angle D$$
Therefore, the correct answer is:
C) $$\angle A$$ and $$\angle C$$
Q4. A student wants to construct a quadrilateral using a diagonal as the common side of two triangles. What is the main advantage of this method?
A) It changes the quadrilateral into a circle
B) It reduces the construction to constructing two triangles
C) It eliminates all measurements
D) It requires no geometrical instruments
Answer:
B) It reduces the construction to constructing two triangles
Useful Concept
A diagonal divides a quadrilateral into two triangles, making the construction easier when suitable measurements are available.
Solution
Suppose quadrilateral:
$$ABCD$$
has diagonal:
$$AC$$
The diagonal divides it into:
$$\triangle ABC$$
and:
$$\triangle ACD$$
Thus, instead of constructing the entire quadrilateral at once, we can construct the two triangles using the given measurements.
Therefore, the main advantage is that the construction is reduced to constructing two triangles.
Hence, the correct answer is:
B) It reduces the construction to constructing two triangles
Q5. During a construction, a student obtains an angle of approximately $$88^\circ$$ when the required angle is $$90^\circ$$. What should the student do?
A) Accept the construction because the difference is small
B) Redraw the angle accurately
C) Change the given side length
D) Ignore the angle
Answer:
B) Redraw the angle accurately
Useful Concept
Geometrical constructions require accurate measurements. Even a small error can affect the final figure.
Solution
The required angle is:
$$90^\circ$$
But the student has constructed approximately:
$$88^\circ$$
The two measurements are not equal:
$$88^\circ\ne90^\circ$$
Therefore, the angle should be corrected and constructed accurately using the appropriate instrument.
Hence, the correct answer is:
B) Redraw the angle accurately
Important Concepts
Sum of Angles of a Quadrilateral
The sum of the four interior angles is:
$$360^\circ$$
Opposite Angles
For quadrilateral:
$$ABCD$$
the opposite angle pairs are:
$$\angle A \text{ and } \angle C$$
and:
$$\angle B \text{ and } \angle D$$
Diagonal Construction
A diagonal divides a quadrilateral into two triangles.
For example:
$$ABCD \rightarrow \triangle ABC+\triangle ACD$$
Construction Accuracy
Given measurements should be followed accurately. An incorrect length or angle can change the final shape.
Use of Geometrical Instruments
✔ Ruler — line segments and lengths
✔ Compass — arcs and transfer of lengths
✔ Protractor — angles
Related Practice Questions
Q1. Find the fourth angle of a quadrilateral if three angles are:
$$70^\circ,\ 90^\circ,\ 110^\circ$$
Q2. What is the sum of the interior angles of a quadrilateral?
Q3. In quadrilateral $$PQRS$$, name the opposite angles.
Q4. Why is a diagonal useful in quadrilateral construction?
Q5. What should you do if your constructed length does not match the given measurement?
Mini Quiz Challenge
Try answering these questions within 60 seconds.
Q1. The sum of the angles of a quadrilateral is:
A) $$180^\circ$$
B) $$270^\circ$$
C) $$360^\circ$$
D) $$540^\circ$$
Q2. If three angles are:
$$75^\circ,\ 85^\circ,\ 100^\circ$$
the fourth angle is:
A) $$90^\circ$$
B) $$100^\circ$$
C) $$110^\circ$$
D) $$120^\circ$$
Q3. Which pair consists of opposite angles in quadrilateral $$PQRS$$?
A) $$\angle P,\angle Q$$
B) $$\angle Q,\angle R$$
C) $$\angle P,\angle R$$
D) $$\angle R,\angle S$$
Q4. A diagonal of a quadrilateral creates:
A) Two triangles
B) Three triangles
C) Four triangles
D) One circle
Q5. If the required angle is:
$$60^\circ$$
but the constructed angle is:
$$65^\circ$$
what should be done?
A) Keep it unchanged
B) Correct the construction
C) Change the diagonal
D) Remove the angle
Exam Tips
✔ Remember that the angle sum of a quadrilateral is $$360^\circ$$.
✔ Learn the difference between adjacent and opposite angles.
✔ Use diagonals to understand quadrilateral construction.
✔ Check every measurement before finalising the construction.
✔ Do not accept approximate measurements when an exact value is required.
✔ Keep construction lines neat and visible while checking the figure.
Quick Revision Notes
✔ Quadrilateral has four interior angles.
✔ Sum of interior angles:
$$360^\circ$$
✔ Opposite angles do not share a common side.
✔ A diagonal divides a quadrilateral into two triangles.
✔ Ruler is used for line segments.
✔ Compass is used for arcs and transferring lengths.
✔ Protractor is used for measuring and constructing angles.
✔ Accuracy is essential in practical geometry.
Common Mistakes Students Make
❌ Using $$180^\circ$$ as the angle sum of a quadrilateral.
❌ Confusing opposite angles with adjacent angles.
❌ Ignoring small errors in construction.
❌ Measuring an angle from the wrong scale of a protractor.
❌ Forgetting to check the completed figure against the given conditions.
Key Takeaways
✔ The interior angles of a quadrilateral add up to:
$$360^\circ$$
✔ Opposite angles are located at opposite vertices.
✔ A diagonal divides a quadrilateral into two triangles.
✔ Construction measurements must be accurate.
✔ Errors in lengths or angles can change the shape of the constructed figure.
✔ Proper use of ruler, compass, and protractor is essential.
FAQs
Q. What is the sum of the interior angles of a quadrilateral?
Answer:
The sum of the four interior angles of a quadrilateral is:
$$360^\circ$$
Q. What are opposite angles?
Answer:
Opposite angles are angles that do not share a common side. In quadrilateral:
$$ABCD$$
the opposite pairs are:
$$\angle A,\angle C$$
and:
$$\angle B,\angle D$$
Q. Why is a diagonal useful in construction?
Answer:
A diagonal divides a quadrilateral into two triangles. This makes it easier to construct the quadrilateral using suitable measurements.
Q. What should be done if a construction measurement is incorrect?
Answer:
The incorrect part should be checked and constructed again using the correct measurement.
Q. Why is accuracy important in practical geometry?
Answer:
Accuracy ensures that the constructed figure satisfies the lengths and angles specified in the question.
Conclusion
Class 8 Maths Chapter 4 Practical Geometry MCQ provides fresh NCERT-based practice on angle sums, opposite angles, diagonal-based construction, and accuracy in geometrical constructions.
Related links
- Class 8 Science Chapter 1 Crop Production and Management part-10
- Class 8 English Chapter 1 Another Chance part-6
- Class 8 Social Science Chapter 1 How, When and Where part-9
- Class 8 Maths Chapter 4 Practical Geometry part-3
- Class 8 Science Chapter 1 Crop Production and Management part-9
- Class 8 English Chapter 1 Another Chance part-5
- Class 8 Social Science Chapter 1 How, When and Where part-8
- Class 8 Maths Chapter 4 Practical Geometry part-2
- Class 8 Science Chapter 1 Crop Production and Management part-8
- Class 8 English Chapter 1 Another Chance psrt-4
- Class 8 Social Science Chapter 1 How, When and Where part-8
- Class 8 Science Chapter 1 Crop Production and Management part-7
- Class 8 Maths Chapter 4 Practical Geometry part-1
- Class 8 Social Science Chapter 1 How, When and Where part-7
Latest Posts
- Class 9 Maths Chapter 4 Linear Equations in Two Variables
- Class 7 Maths Chapter 4 Simple Equations
- Class 8 Maths Chapter 4 Practical Geometry
- Class 10 Maths Chapter 4 Quadratic Equations
- Class 9 Science Chapter 1 Matter in Our Surroundings
Join Our Other Communities
Instagram , Youtube , Facebook
