Angles and Parallel Lines - Applications MCQ & Objective Questions
Understanding "Angles and Parallel Lines - Applications" is crucial for students preparing for various exams. This topic not only forms the foundation of geometry but also plays a significant role in solving objective questions effectively. Practicing MCQs and important questions related to this topic can significantly enhance your exam preparation and boost your confidence.
What You Will Practise Here
Identifying types of angles formed by parallel lines and transversals
Understanding the properties of alternate interior and exterior angles
Applying the concept of corresponding angles in problem-solving
Using angle relationships to find unknown angles in geometric figures
Solving real-life problems involving angles and parallel lines
Interpreting and drawing diagrams related to angles and parallel lines
Reviewing key formulas and definitions related to angles
Exam Relevance
The topic of "Angles and Parallel Lines - Applications" is frequently tested in CBSE, State Boards, and competitive exams like NEET and JEE. Students can expect questions that require them to identify angle relationships, apply properties of parallel lines, and solve for unknown angles. Common question patterns include multiple-choice questions that assess both conceptual understanding and practical application of theorems.
Common Mistakes Students Make
Confusing alternate interior angles with alternate exterior angles
Overlooking the importance of transversal lines in angle relationships
Failing to apply the correct properties when solving for unknown angles
Misinterpreting diagrams, leading to incorrect conclusions
FAQs
Question: What are alternate interior angles? Answer: Alternate interior angles are pairs of angles that lie on opposite sides of a transversal and inside the two parallel lines. They are equal when the lines are parallel.
Question: How can I improve my understanding of angles and parallel lines? Answer: Regular practice of MCQs and solving important questions will help reinforce your understanding and application of concepts related to angles and parallel lines.
Don't miss out on the opportunity to enhance your skills! Start solving practice MCQs on "Angles and Parallel Lines - Applications" today and test your understanding to excel in your exams.
Q. If angle 4 is 110 degrees and is an exterior angle formed by a transversal intersecting two parallel lines, what is the measure of the corresponding interior angle?
A.
70 degrees
B.
110 degrees
C.
90 degrees
D.
180 degrees
Solution
The corresponding interior angle is supplementary to the exterior angle, so 180 - 110 = 70 degrees.
Q. If angle A and angle B are alternate exterior angles formed by a transversal cutting two parallel lines, and angle A measures 50 degrees, what is the measure of angle B?
A.
50 degrees
B.
130 degrees
C.
90 degrees
D.
180 degrees
Solution
Alternate exterior angles are equal, so angle B also measures 50 degrees.
Q. If angle A and angle B are alternate interior angles formed by a transversal intersecting two parallel lines, and angle A measures 75 degrees, what is the measure of angle B?
A.
75 degrees
B.
105 degrees
C.
90 degrees
D.
180 degrees
Solution
Alternate interior angles are equal, so angle B also measures 75 degrees.
Q. If angle A and angle B are same-side interior angles formed by a transversal cutting two parallel lines, and angle A measures 75 degrees, what is the measure of angle B?
A.
75 degrees
B.
105 degrees
C.
90 degrees
D.
180 degrees
Solution
Same-side interior angles are supplementary, so angle B = 180 - 75 = 105 degrees.
Q. If two lines are parallel and a transversal creates an angle of 120 degrees with one of the lines, what is the measure of the corresponding angle on the other line?
A.
60 degrees
B.
120 degrees
C.
180 degrees
D.
90 degrees
Solution
Corresponding angles are equal, so the corresponding angle is also 120 degrees.
Q. If two parallel lines are cut by a transversal and one of the same-side interior angles is 75 degrees, what is the measure of the other same-side interior angle?
A.
75 degrees
B.
105 degrees
C.
90 degrees
D.
180 degrees
Solution
Same-side interior angles are supplementary, so the other angle measures 105 degrees.
Q. If two parallel lines are intersected by a transversal and one of the interior angles is 70 degrees, what is the measure of the other interior angle on the same side of the transversal?
A.
70 degrees
B.
110 degrees
C.
180 degrees
D.
90 degrees
Solution
Interior angles on the same side of the transversal are supplementary, so 180 - 70 = 110 degrees.
Q. If two parallel lines are intersected by a transversal and one of the interior angles measures 70 degrees, what is the measure of the other interior angle on the same side of the transversal?
A.
70 degrees
B.
110 degrees
C.
180 degrees
D.
90 degrees
Solution
Interior angles on the same side of the transversal are supplementary, so 180 - 70 = 110 degrees.
Q. In a transversal intersecting two parallel lines, if one of the alternate interior angles is 35 degrees, what is the measure of the other alternate interior angle?
A.
35 degrees
B.
145 degrees
C.
90 degrees
D.
180 degrees
Solution
Alternate interior angles are equal, so the other angle is also 35 degrees.
Q. In a transversal intersecting two parallel lines, if one of the alternate interior angles measures 35 degrees, what is the measure of the other alternate interior angle?
A.
35 degrees
B.
145 degrees
C.
90 degrees
D.
180 degrees
Solution
Alternate interior angles are equal, so the other angle also measures 35 degrees.
Q. In a transversal intersecting two parallel lines, if one of the corresponding angles measures 75 degrees, what is the measure of the other corresponding angle?
A.
75 degrees
B.
105 degrees
C.
90 degrees
D.
180 degrees
Solution
Corresponding angles are equal, so the other corresponding angle also measures 75 degrees.
Q. In a transversal intersecting two parallel lines, if one of the interior angles is 30 degrees, what is the measure of the exterior angle adjacent to it?
A.
30 degrees
B.
150 degrees
C.
90 degrees
D.
60 degrees
Solution
The exterior angle is supplementary to the interior angle, so 180 - 30 = 150 degrees.
Q. What is the relationship between the exterior angle and the two interior opposite angles in a triangle formed by a transversal intersecting two parallel lines?
A.
The exterior angle is equal to the sum of the two interior opposite angles.
B.
The exterior angle is less than the sum of the two interior opposite angles.
C.
The exterior angle is greater than the sum of the two interior opposite angles.
D.
There is no relationship.
Solution
The exterior angle is equal to the sum of the two interior opposite angles in a triangle.
Correct Answer:
A
— The exterior angle is equal to the sum of the two interior opposite angles.
