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Practise Class 7 Maths Chapter 5 MCQs Set 3 on angles formed by intersecting lines, angle bisectors, straight angles, and complementary angles with detailed solutions.
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Chapter Information
- Class: 7
- Subject: Mathematics
- Chapter: 5 – Parallel and Intersecting Lines
- Practice Set: 3
- Board: CBSE
- Textbook Reference: NCERT Ganita Prakash
- Question Type: Multiple-Choice Questions (MCQs)
Introduction
Lines and angles are essential concepts in geometry. When straight lines intersect, they form angles that follow specific mathematical properties. Understanding these properties helps students calculate unknown angles and solve geometric problems.
This practice set covers angle bisectors, complementary angles, straight angles, and relationships between angles formed by intersecting lines. All questions and explanations are independently written for educational practice.
What Will You Learn?
After completing this practice set, students will be able to:
- Understand the meaning of an angle bisector.
- Calculate complementary angles.
- Apply the properties of straight angles.
- Find unknown angles formed by intersecting lines.
- Recognise different types of angles.
Why Is This Topic Important?
Angle properties help students develop logical reasoning and accuracy in mathematics. These concepts are useful when studying geometrical constructions, triangles, polygons, and other shapes.
Exam Relevance
Questions from this topic may involve:
- Finding the bisector of an angle.
- Calculating complementary angles.
- Using the angle properties of intersecting lines.
- Finding missing angles on a straight line.
- Classifying angles by their measurements.
MCQs with Detailed Solutions
Question 1: Understanding an Angle Bisector
An angle measures $$84^\circ$$. A ray divides this angle into two equal parts. What is the measure of each smaller angle?
A. $$32^\circ$$
B. $$42^\circ$$
C. $$48^\circ$$
D. $$84^\circ$$
Answer: B. $$42^\circ$$
Concept: Angle bisector.
Formula:
An angle bisector divides an angle into two equal angles.
$$\text{Each angle}=\frac{\text{Original angle}}{2}$$
Solution:
The original angle measures:
$$84^\circ$$
Since the angle is divided into two equal parts:
$$\frac{84^\circ}{2}=42^\circ$$
Therefore, each smaller angle measures $$42^\circ$$.
Correct Answer: B. $$42^\circ$$
Question 2: Complementary Angles
Two angles are complementary. If one angle measures $$37^\circ$$, what is the measure of the other angle?
A. $$43^\circ$$
B. $$53^\circ$$
C. $$63^\circ$$
D. $$143^\circ$$
Answer: B. $$53^\circ$$
Concept: Complementary angles.
Formula:
The sum of two complementary angles is:
$$\text{Angle 1}+\text{Angle 2}=90^\circ$$
Solution:
Let the unknown angle be $$x$$.
$$37^\circ+x=90^\circ$$
Subtract $$37^\circ$$ from both sides:
$$x=90^\circ-37^\circ$$
$$x=53^\circ$$
Therefore, the other angle measures $$53^\circ$$.
Correct Answer: B. $$53^\circ$$
Question 3: Angles on a Straight Line
Three adjacent angles on a straight line measure $$45^\circ$$, $$65^\circ$$, and $$x^\circ$$. Find the value of $$x$$.
A. $$60^\circ$$
B. $$70^\circ$$
C. $$80^\circ$$
D. $$90^\circ$$
Answer: B. $$70^\circ$$
Concept: Angles on a straight line.
Formula:
The sum of angles forming a straight angle is:
$$180^\circ$$
Solution:
The three adjacent angles form a straight angle.
Therefore:
$$45^\circ+65^\circ+x=180^\circ$$
Add the known angles:
$$110^\circ+x=180^\circ$$
Subtract $$110^\circ$$ from both sides:
$$x=180^\circ-110^\circ$$
$$x=70^\circ$$
Correct Answer: B. $$70^\circ$$
Question 4: Finding an Unknown Angle
Two straight lines intersect. One angle measures $$4x^\circ$$, and its vertically opposite angle measures $$(2x+50)^\circ$$. Find the value of $$x$$.
A. $$20$$
B. $$25$$
C. $$30$$
D. $$35$$
Answer: B. $$25$$
Concept: Vertically opposite angles.
Explanation:
Vertically opposite angles are equal.
Therefore:
$$4x=2x+50$$
Subtract $$2x$$ from both sides:
$$2x=50$$
Divide both sides by $$2$$:
$$x=\frac{50}{2}$$
$$x=25$$
The measure of each of the given opposite angles is:
$$4x=4\times25=100^\circ$$
Checking the other expression:
$$2x+50=2\times25+50=100^\circ$$
Both angles are equal, as expected.
Correct Answer: B. $$25$$
Question 5: Identifying an Obtuse Angle
Which of the following is an obtuse angle?
A. $$28^\circ$$
B. $$90^\circ$$
C. $$124^\circ$$
D. $$180^\circ$$
Answer: C. $$124^\circ$$
Concept: Classification of angles.
Explanation:
An obtuse angle is greater than $$90^\circ$$ but less than $$180^\circ$$.
Check the options:
- $$28^\circ$$ is an acute angle.
- $$90^\circ$$ is a right angle.
- $$124^\circ$$ is an obtuse angle.
- $$180^\circ$$ is a straight angle.
Therefore, $$124^\circ$$ is the obtuse angle.
Correct Answer: C. $$124^\circ$$
Important Formulas & Concepts
1. Angle Bisector
An angle bisector divides an angle into two equal parts.
$$\text{Each part}=\frac{\text{Original angle}}{2}$$
2. Complementary Angles
Two complementary angles have a sum of $$90^\circ$$.
$$\angle A+\angle B=90^\circ$$
3. Angles on a Straight Line
Angles forming a straight angle add up to $$180^\circ$$.
$$\angle 1+\angle 2+\angle 3=180^\circ$$
This applies when the angles together form one straight angle.
4. Vertically Opposite Angles
Vertically opposite angles are equal.
$$\angle A=\angle C$$
5. Types of Angles
- Acute angle: Greater than $$0^\circ$$ and less than $$90^\circ$$.
- Right angle: Exactly $$90^\circ$$.
- Obtuse angle: Greater than $$90^\circ$$ and less than $$180^\circ$$.
- Straight angle: Exactly $$180^\circ$$.
Related Practice Questions
Try solving these questions independently.
- An angle of $$96^\circ$$ is divided into two equal parts. Find each part.
- Find the complement of an angle measuring $$41^\circ$$.
- Two adjacent angles on a straight line measure $$x^\circ$$ and $$132^\circ$$. Find $$x$$.
- If vertically opposite angles are represented by $$3x+10$$ and $$5x-30$$ degrees, find $$x$$.
- Classify an angle measuring $$156^\circ$$.
Mini Quiz Challenge
Question 1
What is the sum of two complementary angles?
A. $$45^\circ$$
B. $$90^\circ$$
C. $$180^\circ$$
D. $$360^\circ$$
Answer: B. $$90^\circ$$
Question 2
Which angle is a straight angle?
A. $$45^\circ$$
B. $$90^\circ$$
C. $$135^\circ$$
D. $$180^\circ$$
Answer: D. $$180^\circ$$
Question 3
A ray divides an angle of $$70^\circ$$ into two equal parts. What is the measure of each part?
A. $$25^\circ$$
B. $$30^\circ$$
C. $$35^\circ$$
D. $$40^\circ$$
Answer: C. $$35^\circ$$
Exam Tips
- Remember that complementary angles add up to $$90^\circ$$.
- A straight angle measures $$180^\circ$$.
- An angle bisector creates two equal angles.
- Vertically opposite angles are equal.
- Identify the type of angle before solving a problem.
- Substitute the calculated value back into the original equation to check your answer.
Quick Revision Notes
- An angle bisector divides an angle into two equal parts.
- Complementary angles have a sum of $$90^\circ$$.
- Angles on a straight line add up to $$180^\circ$$.
- Vertically opposite angles are equal.
- An obtuse angle is greater than $$90^\circ$$ but less than $$180^\circ$$.
- A straight angle measures $$180^\circ$$.
Common Mistakes Students Make
- Confusing complementary angles with supplementary angles.
- Dividing an angle incorrectly when using an angle bisector.
- Forgetting that angles on a straight line total $$180^\circ$$.
- Assuming that adjacent angles are always equal.
- Forgetting to check an algebraic answer in the original equation.
Key Takeaways
Angle bisectors, complementary angles, and vertically opposite angles are important concepts in geometry. By understanding how angles are divided and how their measures are related, students can calculate unknown angles and solve problems with greater confidence.
FAQs
1. What is an angle bisector?
An angle bisector is a ray that divides an angle into two equal angles.
2. What are complementary angles?
Two angles are complementary when their measures add up to $$90^\circ$$.
3. What is the measure of a straight angle?
A straight angle measures $$180^\circ$$.
4. How can an unknown angle on a straight line be found?
Subtract the sum of the known angles from $$180^\circ$$.
5. How are vertically opposite angles related?
They are equal when two straight lines intersect.
Conclusion
This practice set covers angle bisectors, complementary angles, straight angles, vertically opposite angles, and the classification of angles. Students can strengthen their geometry skills by practising the questions and checking each solution carefully.
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