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Test: Lines & Angles- Case Based Type Questions - EmSAT Achieve MCQ


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10 Questions MCQ Test - Test: Lines & Angles- Case Based Type Questions

Test: Lines & Angles- Case Based Type Questions for EmSAT Achieve 2024 is part of EmSAT Achieve preparation. The Test: Lines & Angles- Case Based Type Questions questions and answers have been prepared according to the EmSAT Achieve exam syllabus.The Test: Lines & Angles- Case Based Type Questions MCQs are made for EmSAT Achieve 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Lines & Angles- Case Based Type Questions below.
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Test: Lines & Angles- Case Based Type Questions - Question 1

Direction: BSE stands for a disease called Bovine Spongiform Encephalopathy. “Bovine” means that the disease affects cows, “spongiform” refers to the way the brain from a sick cow looks spongy under a microscope, and “encephalopathy” indicates that it is a disease of the brain. This disease is commonly called “mad cow disease.”

A farmer has a field ABCD formed by two pair of parallel roads as shown below in which l ||m and p || q. His four cows suffering from BSE. Thus, he tied them at four corners of the field ABCD.

Q. If ∠BAC = 30°, find ∠ACD.

Detailed Solution for Test: Lines & Angles- Case Based Type Questions - Question 1
p||q and AC is a transversal. Thus, DBAC and ∠ACD are alternate interior angles. Therefore, ∠BAC = ∠ACD = 30° (alternate interior angles are equal).
Test: Lines & Angles- Case Based Type Questions - Question 2

Direction: BSE stands for a disease called Bovine Spongiform Encephalopathy. “Bovine” means that the disease affects cows, “spongiform” refers to the way the brain from a sick cow looks spongy under a microscope, and “encephalopathy” indicates that it is a disease of the brain. This disease is commonly called “mad cow disease.”

A farmer has a field ABCD formed by two pair of parallel roads as shown below in which l ||m and p || q. His four cows suffering from BSE. Thus, he tied them at four corners of the field ABCD.

Q. ∠ABC + ∠BCD = 180° as :

Detailed Solution for Test: Lines & Angles- Case Based Type Questions - Question 2
Angles on the same side of a transversal are supplementary.
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Test: Lines & Angles- Case Based Type Questions - Question 3

Direction: BSE stands for a disease called Bovine Spongiform Encephalopathy. “Bovine” means that the disease affects cows, “spongiform” refers to the way the brain from a sick cow looks spongy under a microscope, and “encephalopathy” indicates that it is a disease of the brain. This disease is commonly called “mad cow disease.”

A farmer has a field ABCD formed by two pair of parallel roads as shown below in which l ||m and p || q. His four cows suffering from BSE. Thus, he tied them at four corners of the field ABCD.

Q. If cow at C and cow at D is 2 km apart, then what is the distance between cow at A and cow at B?

Detailed Solution for Test: Lines & Angles- Case Based Type Questions - Question 3
Since, p||q and l||m thus, ABCD is a parallelogram. Also, since opposite sides of a parallelogram are equal.

So, AB = CD

Given, distance between cow at C and cow at D = CD = 2 km

⇒ AB = 2 km

Hence distance between cow at A and cow at B is 2 km.

Test: Lines & Angles- Case Based Type Questions - Question 4

Direction: BSE stands for a disease called Bovine Spongiform Encephalopathy. “Bovine” means that the disease affects cows, “spongiform” refers to the way the brain from a sick cow looks spongy under a microscope, and “encephalopathy” indicates that it is a disease of the brain. This disease is commonly called “mad cow disease.”

A farmer has a field ABCD formed by two pair of parallel roads as shown below in which l ||m and p || q. His four cows suffering from BSE. Thus, he tied them at four corners of the field ABCD.

Q. If ∠B = 45°, then ∠D = _________ .

Detailed Solution for Test: Lines & Angles- Case Based Type Questions - Question 4
Since, ∠B =45°

⇒ ∠D =45°

(opposite angles of a parallelogram are equal)

Test: Lines & Angles- Case Based Type Questions - Question 5

Direction: BSE stands for a disease called Bovine Spongiform Encephalopathy. “Bovine” means that the disease affects cows, “spongiform” refers to the way the brain from a sick cow looks spongy under a microscope, and “encephalopathy” indicates that it is a disease of the brain. This disease is commonly called “mad cow disease.”

A farmer has a field ABCD formed by two pair of parallel roads as shown below in which l ||m and p || q. His four cows suffering from BSE. Thus, he tied them at four corners of the field ABCD.

Q. If we join BD such that BD meet AC at O and ∠BOC = 30°, then what is the measure of ∠AOD?

Detailed Solution for Test: Lines & Angles- Case Based Type Questions - Question 5
∠BOC = ∠ AOD = 30

(vertically opposite angles are equal)

Test: Lines & Angles- Case Based Type Questions - Question 6

Direction: A plane mirror is a mirror with a flat reflective surface.

An incident ray is a ray of light that strikes a surface. The reflected ray corresponding to a given incident ray, is the ray that represents the light reflected by the surface. In figure, m and n are two plane mirrors perpendicular to each other.

Q. Parallel lines :

Detailed Solution for Test: Lines & Angles- Case Based Type Questions - Question 6
Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Test: Lines & Angles- Case Based Type Questions - Question 7

Direction: A plane mirror is a mirror with a flat reflective surface.

An incident ray is a ray of light that strikes a surface. The reflected ray corresponding to a given incident ray, is the ray that represents the light reflected by the surface. In figure, m and n are two plane mirrors perpendicular to each other.

Q. If BO = 3 cm, AB = 5 cm then, AO =

Detailed Solution for Test: Lines & Angles- Case Based Type Questions - Question 7
m and n are two plane mirrors perpendicular to each other.

So, AO is perpendicular to BO.

Thus, triangle AOB is a right-angled triangle.

OA2 + OB2 = AB2

OA2 + 32 = 52

OA2 + 9 = 25

OA2 = 25 – 9 = 16

OA = 4 cm

Test: Lines & Angles- Case Based Type Questions - Question 8

Direction: A plane mirror is a mirror with a flat reflective surface.

An incident ray is a ray of light that strikes a surface. The reflected ray corresponding to a given incident ray, is the ray that represents the light reflected by the surface. In figure, m and n are two plane mirrors perpendicular to each other.

Q. Which statement is incorrect ?

Detailed Solution for Test: Lines & Angles- Case Based Type Questions - Question 8
We know, two distinct parallel lines having interior angles on the same side of the transversal are supplementary angles(having sum equal to 180o . So, obviously they cannot be complementary angles (having sum equal to 90o) So, the statement is incorrect.
Test: Lines & Angles- Case Based Type Questions - Question 9

Direction: A plane mirror is a mirror with a flat reflective surface.

An incident ray is a ray of light that strikes a surface. The reflected ray corresponding to a given incident ray, is the ray that represents the light reflected by the surface. In figure, m and n are two plane mirrors perpendicular to each other.

Q. ∠DBA + ∠BAC

Detailed Solution for Test: Lines & Angles- Case Based Type Questions - Question 9
Since, AC is parallel to BD. Also, ∠DBA and ∠BAC are on same side of transversal AB.

Therefore, they are supplementary.

Hence, ∠DBA + ∠BAC = 180°

Test: Lines & Angles- Case Based Type Questions - Question 10

Direction: A plane mirror is a mirror with a flat reflective surface.

An incident ray is a ray of light that strikes a surface. The reflected ray corresponding to a given incident ray, is the ray that represents the light reflected by the surface. In figure, m and n are two plane mirrors perpendicular to each other.

Q. Incident ray CA is :

Detailed Solution for Test: Lines & Angles- Case Based Type Questions - Question 10
Let normals at A and B meet at P.

As mirrors are perpendicular to each other, therefore, BP || OA and AP || OB.

So, BP ⊥ PA, i.e., ∠ BPA = 90°

Therefore, ∠ 3 + ∠ 2 = 90° (Angle sum property) (1)

Also, ∠1 = ∠2 and ∠4 = ∠3 (Angle of incidence = Angle of reflection)

Therefore, ∠1 + ∠4 = 90° [From (1)] (2) Adding (1) and (2), we have

∠1 + ∠2 + ∠3 + ∠4 = 180°

i.e., ∠CAB + ∠DBA = 180°

Hence, CA || BD

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