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Important Questions: The Triangle and Its Properties - Class 7 MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 7 - Important Questions: The Triangle and Its Properties

Important Questions: The Triangle and Its Properties for Class 7 2024 is part of Mathematics (Maths) Class 7 preparation. The Important Questions: The Triangle and Its Properties questions and answers have been prepared according to the Class 7 exam syllabus.The Important Questions: The Triangle and Its Properties MCQs are made for Class 7 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Important Questions: The Triangle and Its Properties below.
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Important Questions: The Triangle and Its Properties - Question 1

Find the measure of the angle x in the given figure.

                           

Detailed Solution for Important Questions: The Triangle and Its Properties - Question 1

∠EFD+∠FED = x  
(Exterior angle property of a triangle) 
⇒ 28o+42= ∠x or ∠x = 70o

Important Questions: The Triangle and Its Properties - Question 2

In the figure (not drawn to scale), ABC is an equilateral triangle and ABD is an isosceles triangle with DA = DB, find x. 

Detailed Solution for Important Questions: The Triangle and Its Properties - Question 2

Since ABC is an equilateral triangle. 
∴ ∠CAB =∠ABC =∠BCA = 60 
And ∠DBA = ∠DAB = (60o−x) 
[∵ DA = DB] 
In ΔDAB, ∠DAB∠DAB+∠ADB =180  
⇒ 2(60o−x)+88= 180o 
⇒ 2(60o−x) = 92o
⇒ 60o−x = 46⇒ x = 14o

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Important Questions: The Triangle and Its Properties - Question 3

ABC is an isosceles triangle with AB = AC and AD is altitude, then ____.

Detailed Solution for Important Questions: The Triangle and Its Properties - Question 3

Explanation: In an isosceles triangle, the angles opposite the equal sides are also equal. Since AB = AC in triangle ABC, the angles opposite these sides, which are ∠B and ∠C, must be equal. Additionally, AD being the altitude means it is also the angle bisector, further ensuring that ∠B = ∠C

 

Important Questions: The Triangle and Its Properties - Question 4

In the following figure, the measure of ∠A is

Detailed Solution for Important Questions: The Triangle and Its Properties - Question 4

Important Questions: The Triangle and Its Properties - Question 5

Find the measure of the angle x in the given figure.  

                                  

Detailed Solution for Important Questions: The Triangle and Its Properties - Question 5

∠UXV = y (Vertically opposite angles) 
∴ y = 45In ΔXYZ y+x+63o = 180 
(Angle sum property) 
⇒ 45o+x+63= 180o
⇒ x = 180o−(45o+63o
⇒  x= 180o−108= 72o

Important Questions: The Triangle and Its Properties - Question 6

In the following figure, m || QR. Then, the measure of ∠QPR is

Detailed Solution for Important Questions: The Triangle and Its Properties - Question 6

 

Important Questions: The Triangle and Its Properties - Question 7

In the following figure, find ∠ x and ∠ y, if ∠x – ∠y = 10°

Detailed Solution for Important Questions: The Triangle and Its Properties - Question 7

 

Important Questions: The Triangle and Its Properties - Question 8

Classify the following triangle on basis of their sides 

Detailed Solution for Important Questions: The Triangle and Its Properties - Question 8

(i) PQ = 5 cm, PR = 6 cm and QR = 7 cm
PQ ≠ PR ≠ QR
Thus, ∆PQR is a scalene triangle.
(ii) AB = 4 cm, AC = 4 cm
AB = AC
Thus, ∆ABC is an isosceles triangle.
(iii) MN = 3 cm, ML = 3 cm and NL = 3 cm
MN = ML = NL
Thus, ∆MNL is an equilateral triangle.

Important Questions: The Triangle and Its Properties - Question 9

In the given figure, find x.

Detailed Solution for Important Questions: The Triangle and Its Properties - Question 9

In ∆ABC, we have
5x – 60° + 2x + 40° + 3x – 80° = 180° (Angle sum property of a triangle)
⇒ 5x + 2x + 3x – 60° + 40° – 80° = 180°
⇒ 10x – 100° = 180°
⇒ 10x = 180° + 100°
⇒ 10x = 280°
⇒ x = 28°
Thus, x = 28°

Important Questions: The Triangle and Its Properties - Question 10

Find the measure of ∠LNM in the given figure.

Detailed Solution for Important Questions: The Triangle and Its Properties - Question 10

∠KLO = ∠MLN 
∴ ∠MLN = 70o in ∠LMN,∠MLN+∠LNM+∠LMN = 180
(Angle sum property) 
⇒ 70o+∠LNM+50o=180o
 
⇒ ∠LNM = 180o−(70o+50o) = 60o

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