Important Lines and Angles Multiple Choice Questions with Concepts and Explanations
Geometry has always been an exciting and vital topic of mathematics. The Lines and Angles chapter of Class 9 Mathematics introduces you to essential geometry chapters. We know that angles are formed when any two lines intersect or meet. MCQ on Lines and Angles Class 9 chapter focuses mainly on the properties of angles formed in two conditions:
When two lines intersect each other.
When a line crosses two or more parallel lines.
In some more detail, let us look up NCERT Class 9 Lines and Angles MCQs in this chapter. We know that the base of the chapter must be crystal clear to understand each topic in detail and in the best way possible. We have to be clear with basic terms and definitions and the difference between them, such as line segment, ray, collinear points, and non-collinear points. Thus, we cover the basics of lines.
Angles
Angles are just like the heart and soul of geometry. An angle is born when two rays originate from a common point or two or more lines intersect. In this chapter, we come across five types of angles. They are:
Acute Angle
An angle is acute when it measures less than 90 degrees but is greater than 0. In short, the acute angle is an angle between 0 and 90 degrees.
0 degree < acute angle < 90 degree
Right Angle
When an angle measures to be an exact 90 degrees, it is called a right angle. It is also called a perpendicular angle.
Obtuse Angle
An obtuse angle always measures to be greater than 90 degrees but less than 180 degrees. All angles between 90 and 180 degrees are obtuse.
90 degree < Obtuse angle < 180 degree
Straight Angle
The angle between a straight line makes up a straight angle. It always measures to be an exact 180 degrees.
Reflex Angle
Angle measuring greater than 180 degrees but less than 360 degrees is called a reflex angle. All reflex angles are situated between 180 and 360 degrees.
180 degree < Reflex angle < 360 degree.
There are also some types of angles that only a pair of angles could make. They are:
Complementary Angles: Two angles that add up to form 90 degrees are called complementary angles. For example, if angle ABC and angle QPR are complementary angles, then; Angle ABC + Angle QPR = 90 degrees.
Supplementary Angles: When the sum of two angles makes up 180 degrees, they are supplementary angles. Suppose if angle ABC and angle QPR are supplementary, then:
Angle ABC + Angle QPR = 180 degree
Adjacent Angles: Two angles are said to be adjacent if they satisfy the following conditions:
The two angles must originate from a common vertex.
The two angles must have a common arm.
The two angles' non-common arms are situated on opposite sides of the common arm.
If angle ABD and Angle CBD are two adjacent angles with BD as their common arm, then rays AB and CB must be situated opposite the common arm BD. Also, Angle ABD + Angle CBD = Angle ABC.
Vertically Opposite Angles: When two lines intersect, there form four angles between them. Pair of angles in which one is situated opposite the other forms vertically opposite angles. Vertically opposite angles are always equal.
Intersecting and Non-Intersecting Lines
Discussion about lines cannot be complete without mentioning intersecting and non-intersecting lines. Intersecting lines are those which meet up or cross and pass so that they make angles between them. But, non-intersecting are those that do not meet up or tend to meet at any point. They are also known as parallel lines.
Linear Pair of Angles
Linear pairs of angles are those angles that are situated adjacent to each other and also whose sum equals 180 degrees.
Parallel Lines and Transversal
A single line that intersects two or more lines, that too at distinct points, is said to be a transversal. A transversal intersects parallel and non-parallel lines.
Triangles
Triangles can be considered a section of geometry itself due to their immense properties and theorems. In this chapter, we learn about two properties.
Angle Sum Property of a Triangle
According to the angle sum property of a triangle, the sum of three angles of a triangle always equals 180 degrees.
Exterior Angle Property
According to the exterior angle property, when a side of a triangle is extended, the exterior angle thus formed with the triangle equals the sum of two opposite interior angles.
In Daily Life
The concept of lines and angles, or in short geometry itself, is a widely used part of all our daily lives. We can find different types of lines and angles in most of the things around us. When it comes to constructing a new house, road, or building, irrespective of the construction, we need a plan made of lines and angles. In short, we can find lines and angles in each corner of our lives.
Lines and Angles – MCQs
MCQs can always clarify concepts and help us check our own knowledge of any topic. Lines and Angles Class 9 MCQs can provide an in-depth understanding of how much you have conquered in the topic. Here we provide some examples too.
If ABC and PCQ are vertically opposite angles and ABC measures 60 degrees, how much is PCQ?
90
30
60
45
Ans: C. 60
If the exterior angle of a triangle is 120 degrees and one of its opposite interior angles is 70, how much is the other opposite angle in the triangle
50
120
45
30
Ans: A.50
Multiple Choice Questions
Question 1.
In ΔABC, given that ∠A = 50° and the external bisectors of ∠B and ∠C intersect at point O, then ∠BOC is,
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(a) 40°
(b) 65°
(c) 115°
(d) 140°
Answer: (b) 65°
Question 2.
Calculate the value of x in the following figure.
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(a) 120°
(b) 130°
(c) 110°
(d) 100°
Answer: (b) 130°
Question 3.
An exterior angle of a triangle is 80°. The interior opposite angles are given in the ratio of 1 : 3, then the interior opposite angles are
(a) 30°, 90°
(b) 40°, 120°
(c) 20°, 60°
(d) 30°, 60°
Answer: (c) 20°, 60°
Question 4.
In the given triangle ΔABC, if the bisectors of ∠ABC and ∠BCA intersect at the point O. Then the measure of ∠BOC is,
(a) 90° + ∠A
(b) 90° + ∠A2
(c) 180 – ∠A
(d) 90° – ∠A2
Answer: (b) 90° + ∠A2
Question 5.
In the given figure ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = k right angles, then what is the value of k.
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(а) 2
(b) 3
(c) 4
(d) 5
Answer: (c) 4
Question 6.
From the given figure, the angle ∠ABC is
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(a) 80°
(b) 20°
(c) 100°
(d) 60°
Answer: (a) 80°
Question 7.
Name the type of triangle formed, If the angles of a given triangle are in the ratio of 5 : 3 : 7.
(а) an acute-angled triangle
(b) an obtuse-angled triangle
(c) a right-angled triangle
(d) an isosceles triangle.
Answer: (а) an acute-angled triangle
Question 8.
In the given figure, L1 || L2, then what is the value of x
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(a) 80°
(b) 100°
(c) 110°
(d) 70°
Answer: (a) 80°
Question 9.
If one angle of a triangle is equal to the sum of the other two angles of the same triangle, then the triangle is said to be
(a) an isosceles triangle
(b) an obtuse-angled triangle
(c) an equilateral triangle
(d) a right triangle
Answer: (d) a right triangle
Question 10.
One angle of a triangle is 75°. If the difference of the other two angles of a triangle is 35°, then the biggest angle of the other two angles are
(a) 80°
(b) 75°
(c) 70°
(d) 135°
Answer: (c) 70°
FAQs on Lines and Angles MCQs with Answers and Detailed Solutions
1. What are lines and angles in geometry?
A line is a straight path that extends infinitely in both directions, and an angle is formed when two lines or rays meet at a common point called a vertex. In geometry:
- A line has no thickness and no endpoints.
- A ray has one endpoint and extends infinitely in one direction.
- An angle is measured in degrees (°).
- Angles are formed by two rays sharing a common endpoint called the vertex.
2. What are the different types of angles?
The different types of angles are classified based on their measure in degrees. The main types include:
- Acute angle: Less than 90°
- Right angle: Exactly 90°
- Obtuse angle: Between 90° and 180°
- Straight angle: Exactly 180°
- Reflex angle: Between 180° and 360°
- Complete angle: Exactly 360°
3. What is the sum of angles on a straight line?
The sum of angles on a straight line is always 180°. If two or more angles form a straight line, they are called linear pair angles and their total is 180°.
- Example: If one angle is 110°, the other angle is 180° − 110° = 70°.
4. What is a linear pair of angles?
A linear pair consists of two adjacent angles whose sum is 180°. These angles share:
- A common vertex
- A common arm
- Other arms forming a straight line
5. What are vertically opposite angles?
Vertically opposite angles are the angles formed opposite each other when two lines intersect, and they are always equal. Key properties include:
- They share the same vertex.
- They are equal in measure.
6. What are corresponding angles when a transversal cuts parallel lines?
When a transversal cuts two parallel lines, corresponding angles are equal. These angles:
- Occupy the same relative position at each intersection.
- Are equal only if the lines are parallel.
7. What is the difference between complementary and supplementary angles?
Complementary angles add up to 90°, while supplementary angles add up to 180°. The key differences are:
- Complementary: Sum = 90° (Example: 30° and 60°)
- Supplementary: Sum = 180° (Example: 100° and 80°)
8. How do you find an unknown angle using angle sum property?
You find an unknown angle by subtracting the known angles from the total angle sum. Steps:
- Identify the angle rule (e.g., straight line = 180°).
- Add the known angles.
- Subtract from the total.
x = 180° − 50° = 130°. This method is essential for solving lines and angles MCQs quickly.
9. What happens when a transversal cuts parallel lines?
When a transversal cuts two parallel lines, specific angle pairs become equal or supplementary. The important relationships are:
- Corresponding angles are equal.
- Alternate interior angles are equal.
- Co-interior (consecutive interior) angles sum to 180°.
10. What are common mistakes in solving lines and angles MCQs?
Common mistakes in lines and angles MCQs include misidentifying angle pairs and forgetting basic angle sum rules. Frequent errors are:
- Confusing corresponding and alternate interior angles.
- Forgetting that a straight line equals 180°.
- Assuming lines are parallel without it being stated.
- Miscalculating subtraction in angle sum problems.
