NCERT Class 9 Solutions: Line and Angles (Chapter 6) Exercise 6.2 – Part 1

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Interior, Alternate, Vertically Opposite, Corresponding Angles

Interior, Alternate, Vertically Opposite, Corresponding Angles

Interior, Alternate, Vertically Opposite, Corresponding Angles

Q-1 In the figure, find the value of x and y and then show that ABCD

Angle α Angle α: Angle between A, I, K Angle α Angle α: Angle between A, I, K Angle α Angle α: Angle between A, I, K Angle β Angle β: Angle between J, I, A Angle β Angle β: Angle between J, I, A Angle β Angle β: Angle between J, I, A Angle γ Angle γ: Angle between D, J, I Angle γ Angle γ: Angle between D, J, I Angle γ Angle γ: Angle between D, J, I Angle δ Angle δ: Angle between L, J, C Angle δ Angle δ: Angle between L, J, C Angle δ Angle δ: Angle between L, J, C Vector u Vector u: Vector[A_1, B_1] Vector u Vector u: Vector[A_1, B_1] Vector v Vector v: Vector[A_1, C_1] Vector v Vector v: Vector[A_1, C_1] Vector w Vector w: Vector[D_1, E] Vector w Vector w: Vector[D_1, E] Vector a Vector a: Vector[D_1, F] Vector a Vector a: Vector[D_1, F] Vector b Vector b: Vector[A_1, G] Vector b Vector b: Vector[A_1, G] Vector c Vector c: Vector[A_1, H] Vector c Vector c: Vector[A_1, H] Point A Point A: Point on v Point A Point A: Point on v Point A Point A: Point on v Point B Point B: Point on u Point B Point B: Point on u Point B Point B: Point on u Point D D = (2, 1.46) Point D D = (2, 1.46) Point D D = (2, 1.46) Point C Point C: Point on a Point C Point C: Point on a Point C Point C: Point on a

Lines AB and CD Is Parallel

Line AB and CD parallel to each other. Also given are angles x and y

Solution,

Give line of AB and CD and it is parallel to each other. Also give angle x and y

x+50°=180° (Linear pair)

x=130°

Also,

y=130° (Vertically opposite)

Now,

x=y=130° (Alternate interior angles)

Alternate interior angles are equal. Therefore ,AB CD.

Q-2 In the figure, if ABCD,CDEF and y:z=3:7 find x.

Angle α Angle α: Angle between A, L, M Angle α Angle α: Angle between A, L, M Angle α Angle α: Angle between A, L, M Angle β Angle β: Angle between L, M, C Angle β Angle β: Angle between L, M, C Angle β Angle β: Angle between L, M, C Angle γ Angle γ: Angle between M, N, F Angle γ Angle γ: Angle between M, N, F Angle γ Angle γ: Angle between M, N, F Vector u Vector u: Vector[A_1, B_1] Vector u Vector u: Vector[A_1, B_1] Vector v Vector v: Vector[A_1, C_1] Vector v Vector v: Vector[A_1, C_1] Vector w Vector w: Vector[D_1, E_1] Vector w Vector w: Vector[D_1, E_1] Vector a Vector a: Vector[D_1, F_1] Vector a Vector a: Vector[D_1, F_1] Vector b Vector b: Vector[G, H] Vector b Vector b: Vector[G, H] Vector c Vector c: Vector[G, I] Vector c Vector c: Vector[G, I] Vector d Vector d: Vector[D_1, J] Vector d Vector d: Vector[D_1, J] Vector e Vector e: Vector[D_1, K] Vector e Vector e: Vector[D_1, K] Point A Point A: Point on v Point A Point A: Point on v Point A Point A: Point on v Point C Point C: Point on a Point C Point C: Point on a Point C Point C: Point on a Point E Point E: Point on c Point E Point E: Point on c Point E Point E: Point on c Point B Point B: Point on u Point B Point B: Point on u Point B Point B: Point on u Point D Point D: Point on w Point D Point D: Point on w Point D Point D: Point on w Point F Point F: Point on b Point F Point F: Point on b Point F Point F: Point on b O text1 = "O"

Line AB, CD, EF Is Parallel

Line AB, CD, EF parallel to each other and also given y: z = 3: 7

Solution:

Given, ABCDCDEF

y:z=3:7

Now,

x+y=180° (Angles on the same side of transversal)

Also,

O=z (Corresponding angles) and,

y+O=180° (Linear pair)

y+z=180°

Equation,

y=3x and z=7x

3x+7x=180 ° 10x=180°x=18°

y=3×18°=54° (y=3x) and

z=7×18°=126° (z=7x)

Now, x+y=180 x+54°=180° x=126°

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