Question

In figures 11 and 12 , p parallel to q . Find the value of x , y and z (whichever is requried) ​

Answer 1

It has given that p || q in figure 11 and 12.

To find : The values of x , y and z.

solution : from figure i.

we know sum of all angles of a triangle is 180°.

so, x + 75° + 25° = 180°

⇒x + 100° = 180°

⇒x = 80°

as it has given that p || q.

so, corresponding angles must be equal.

i.e., 25° = y

also you can see, angles x , y and (180° - z) are angles of a triangle.

so, sum of these angles = 180°

⇒x + y + 180° - z = 180°

⇒80° + 25° - z = 0

⇒z = 105°

from figure ii. draw a line in such a way that p || l || q as shown in figure.

alternate interior angles must be equal.

so, 35° = r and 53° = s

now you can see AB is a straight line.

so, r + s + x = 180°

⇒35° + 53° + x = 180°

⇒88° + x = 180°

⇒x = 92°