NCERT Class 9 Solutions: Line and Angles (Chapter 6) Exercise 6.2 – Part 2

Angles on the same side of transversal

Angles on the Same Side of Transversal

Angles on the same side of transversal

Q-3 In the figure, if Equation , Equation and Equation , find Equation and Equation .

Angle α Angle α: Angle between E_1, E, E' Angle α Angle α: Angle between E_1, E, E' Segment f Segment f: Segment [F, E] Segment g Segment g: Segment [E, G] 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] Point F Point F: Point on u Point F Point F: Point on u Point F Point F: Point on u Point E Point E: Point on w Point E Point E: Point on w Point E Point E: Point on w Point G Point G: Point on v Point G Point G: Point on v Point G Point G: Point on v 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 Point D: Point on w Point D Point D: Point on w Point D Point D: Point on w Point C Point C: Point on a Point C Point C: Point on a Point C Point C: Point on a

Point of a, B, C, D, E, F, G and Line AB and CD at Parallel

Point of A, B, C, D, E, F, G and line AB and CD at parallel

Solution:

Given Equation , Equation and Equation

Now,

Equation

Now, Equation (Since Equation and GE is transversal. Alternate interior angles) Equation Equation

Also,

Equation

Equation Equation °

Now, Equation (Linear pair) Equation Equation

Q-4 In the figure, if Equation , Equation and Equation find Equation

Angle α Angle α: Angle between P, Q, R Angle α Angle α: Angle between P, Q, R Angle α Angle α: Angle between P, Q, R Angle β Angle β: Angle between R, S, T Angle β Angle β: Angle between R, S, T Angle β Angle β: Angle between R, S, T Segment f Segment f: Segment [S, R] Segment g Segment g: Segment [R, Q] Vector u Vector u: Vector[S, B] Vector u Vector u: Vector[S, B] Vector v Vector v: Vector[Q, E] Vector v Vector v: Vector[Q, E] Point S S = (0.62, 2.82) Point S S = (0.62, 2.82) Point S S = (0.62, 2.82) Point R R = (-0.44, 0.78) Point R R = (-0.44, 0.78) Point R R = (-0.44, 0.78) Point Q Q = (-1.98, 2) Point Q Q = (-1.98, 2) Point Q Q = (-1.98, 2) Point P Point P: Point on v Point P Point P: Point on v Point P Point P: Point on v Point T Point T: Point on u Point T Point T: Point on u Point T Point T: Point on u

Point P, Q, R, S, T Also PQ Parallel to ST

Point P, Q, R, S, T also PQ parallel to ST

Solution:

Given,

Equation

A line XY parallel to PQ and ST is drawn.

Angle α Angle α: Angle between P, Q, R Angle α Angle α: Angle between P, Q, R Angle α Angle α: Angle between P, Q, R Angle β Angle β: Angle between R, S, T Angle β Angle β: Angle between R, S, T Angle β Angle β: Angle between R, S, T Segment f Segment f: Segment [S, R] Segment g Segment g: Segment [R, Q] Segment h Segment h: Segment [A, C] Vector u Vector u: Vector[S, B] Vector u Vector u: Vector[S, B] Vector v Vector v: Vector[Q, E] Vector v Vector v: Vector[Q, E] Point S S = (0.62, 2.82) Point S S = (0.62, 2.82) Point S S = (0.62, 2.82) Point R R = (-0.44, 0.78) Point R R = (-0.44, 0.78) Point R R = (-0.44, 0.78) Point Q Q = (-1.98, 2) Point Q Q = (-1.98, 2) Point Q Q = (-1.98, 2) Point P Point P: Point on v Point P Point P: Point on v Point P Point P: Point on v Point T Point T: Point on u Point T Point T: Point on u Point T Point T: Point on u X text1 = "X" Y text2 = "Y"

Line XY Parallel to PQ and ST

Line XY parallel to PQ and ST

Equation (Angles on the same side of transversal) Equation

Equation

Also,

Equation (Angles on the same side of transversal) Equation

Equation

Now,

Equation

Equation

Equation

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