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

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Knowing Interior, Alternate, Vertically Opposite and Corresponding Angles

Interior, Alternate, Vertically Opposite, Corresponding Angles

Knowing Interior, Alternate, Vertically Opposite and Corresponding Angles

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

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

Lines AB and CD

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 ,ABCD.

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

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

Line AB,CD,EF

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

Solution:

  • Given, ABCD and CDEF

    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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