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

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

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

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

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

(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.

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°

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