# NCERT Class 9 Solutions: Line and Angles (Chapter 6) Exercise 6.3 – Part 3

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Two angles, formed when a line crosses two other lines, that lie on opposite sides of the transversal line and on opposite relative sides of the other lines. If the two lines crossed are parallel, the alternate angles are equal.

Q-5 In the figure, if then find the values of x and y.

Solution:

Given,

Now, (Alternate angles as QR is transversal)

Also,

Also,(Linea pair)

Now, (Sum of the angles in a quadrilateral)

Q-6 In the figure, the side QR of is produced to a point S. If the bisectors of and meet at point T, then prove that

Solution:

Given,Bisectors of and meet at point T.To prove,

Proof, (Exterior angle of a triangle equals to the sum of the two interior angles) …………equation (1)

Also, (since, the exterior angle is equal to the sum of the two interior opposite angles) (QT is the bisection of and RT is the bisector of

………..equation (2)

Equating (i) and (ii)

Hence, it’s proved.