Question

give the answer for class 7 math ex 6.3 question fourth part 1 question , but the answer should be in detail . if the answer will be in detail i will mark you brainliest​

Answer 1

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Answer 2

Answer:

Question 1.Find the value of unknown x in the following diagrams:

Answer:

(i) In ΔABC,

∠BAC + ∠ACB + ∠ABC = 180∘ [By angle sum property of a triangle]

⇒ x+50∘+60∘=180∘

⇒ x+110∘=180∘ ⇒ x=180∘–110∘=70∘

(ii) In ΔPQR,

∠RPQ + ∠PQR + ∠RPQ = 180∘ [By angle sum property of a triangle]

⇒ 90∘+30∘+x=180∘

⇒ x+120∘=180∘ ⇒ x=180∘–120∘=60∘

(iii) In ΔXYZ,

∠ZXY + ∠XYZ + ∠YZX = 180∘ [By angle sum property of a triangle]

⇒ 30∘+110∘+x=180∘

⇒ x+140∘=180∘ ⇒ x=180∘–140∘=40∘

(iv) In the given isosceles triangle,

x+x+50∘=180∘ [By angle sum property of a triangle]

⇒ 2x+50∘=180∘

⇒ 2x=180∘–50∘ ⇒ 2x=130∘

⇒ x=130∘2=65∘

(v) In the given equilateral triangle,

x+x+x=180∘ [By angle sum property of a triangle]

⇒ 3x=180∘

⇒ x=180∘3=60∘

(vi) In the given right angled triangle,

x+2x+90∘=180∘ [By angle sum property of a triangle]

⇒ 3x+90∘=180∘

⇒ 3x=180∘–90∘ ⇒ 3x=90∘

⇒ x=90∘3=30∘

NCERT Solutions for Class 7 Maths Exercise 6.3

Question 2.Find the values of the unknowns x and y in the following diagrams:

Answer:

(i) 50∘+x=120∘ [Exterior angle property of a Δ ]

⇒ x=120∘–50∘=70∘

Now, 50∘+x+y=180∘ [Angle sum property of a Δ ]

⇒ 50∘+70∘+y=180∘

⇒ 120∘+y=180∘ ⇒ y=180∘–120∘=60∘

(ii) y=80∘ ……….(i) [Vertically opposite angle]

Now, 50∘+x+y=180∘ [Angle sum property of a Δ ]

⇒ 50∘+80∘+y=180∘[From eq. (i)]

⇒ 130∘+y=180∘ ⇒ y=180∘–130∘=50∘

(iii) 50∘+60∘=x [Exterior angle property of a Δ ]

⇒ x=110∘

Now 50∘+60∘+y=180∘ [Angle sum property of a Δ ]

⇒ 110∘+y=180∘

⇒ y=180∘–110∘ ⇒ y=70∘

(iv) x=60∘ ……….(i) [Vertically opposite angle]

Now, 30∘+x+y=180∘ [Angle sum property of a Δ ]

⇒ 50∘+60∘+y=180∘ [From eq. (i)]

⇒ 90∘+y=180∘ ⇒ y=180∘–90∘=90∘

(v) y=90∘ ……….(i) [Vertically opposite angle]

Now, y+x+x=180∘ [Angle sum property of a Δ ]

⇒ 90∘+2x=180∘ [From eq. (i)]

⇒ 2x=180∘–90∘ ⇒ 2x=90∘

⇒ x=90∘2=45∘

(vi) x=y ……….(i) [Vertically opposite angle]

Now, x+x+y=180∘ [Angle sum property of a Δ ]

⇒ 2x+x=180∘ [From eq. (i)]

⇒ 3x=180∘ ⇒ x=180∘3=60∘