NCERT Class 9 Solutions: Line and Angles (Chapter 6) Exercise 6.1 – Part 1

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Line and Angle relationships are given

Line and Angle Relationships Are Given

Line and Angle relationships are given

Q-1 In the figure line ABandCD interacts at O. If AOC+BOE=70° and BOD=40°, find BOE and reflex COE.

Vector u Vector u: Vector[O, B_1] Vector u Vector u: Vector[O, B_1] Vector v Vector v: Vector[O, C_1] Vector v Vector v: Vector[O, C_1] Vector w Vector w: Vector[O, D_1] Vector w Vector w: Vector[O, D_1] Vector a Vector a: Vector[O, E_1] Vector a Vector a: Vector[O, E_1] Vector b Vector b: Vector[O, F] Vector b Vector b: Vector[O, F] Point O O = (0.8, 2.18) Point O O = (0.8, 2.18) Point O O = (0.8, 2.18) 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 b Point E Point E: Point on b Point E Point E: Point on b 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 A Point A: Point on v Point A Point A: Point on v Point A Point A: Point on v

Give Point of a, B, C, D, E, O on Plane

Give point of A, B, C, D, E, O on plane AB and CD interact at O

Solution:

Given, in fig. point of A, B, C, D, E, O on the plane AB and CD interact with O.

AOC+BOE=70°andBOD=40°

Equation, AOC+BOE+COE=180° (Forms a straight line) 70°+COE=180° COE=180°70°=110° also, COE+BOD+BOE=180° (Forms a straight line) 110°+40°+BOE=180° 150°+BOE=180° BOE=180°150°=30°

Q-2 In figure, lines XY and MN intersect at O. If POY=90°anda:b=2:3 , find c

Angle α Angle α: Angle between P, A, Y Angle α Angle α: Angle between P, A, Y Angle α Angle α: Angle between P, A, Y Angle a Angle a: Angle between P, A, M Angle a Angle a: Angle between P, A, M Angle a Angle a: Angle between P, A, M Angle b Angle b: Angle between M, A, X Angle b Angle b: Angle between M, A, X Angle b Angle b: Angle between M, A, X Angle C Angle C: Angle between X, A, N Angle C Angle C: Angle between X, A, N Angle C Angle C: Angle between X, A, N Vector u Vector u: Vector[A, Y] Vector u Vector u: Vector[A, Y] Vector v Vector v: Vector[A, X] Vector v Vector v: Vector[A, X] Vector w Vector w: Vector[A, P] Vector w Vector w: Vector[A, P] Vector a_1 Vector a_1: Vector[A, N] Vector a_1 Vector a_1: Vector[A, N] Vector b_1 Vector b_1: Vector[A, M] Vector b_1 Vector b_1: Vector[A, M] Point A A = (0.96, 2.04) Point A A = (0.96, 2.04) Point A A = (0.96, 2.04) Point Y Y = (4.54, 2.02) Point Y Y = (4.54, 2.02) Point Y Y = (4.54, 2.02) Point X X = (-2.24, 2.02) Point X X = (-2.24, 2.02) Point X X = (-2.24, 2.02) Point P P = (0.98, 5.28) Point P P = (0.98, 5.28) Point P P = (0.98, 5.28) Point N N = (3.56, -0.24) Point N N = (3.56, -0.24) Point N N = (3.56, -0.24) Point M M = (-1.78, 4.68) Point M M = (-1.78, 4.68) Point M M = (-1.78, 4.68)

Give Point X, Y, M, N, P on Angle of a, B, C, O

Give point X, Y, M, N, P on angle of a, b, c, o line XY and MN intersect at O

Given, in figure X, Y, M, N, P at angle of a, b, c, o

POY=90° and a:b=2:3

equation, POY+a+b=180°

90°+a+b=180°

a+b=180°90°=90°

Let a 2x then will b 3x

2x+3x=90° (a=2x&b=3x) 5x=90°x=18°a=2×18°=36°b=3×18°=54°

Also, b+c=180° (Linear Pair) 54°+c=180°c=126°

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