In ∆ABC, DE || BC (Fig. 6.39). Find the values of x, y and z.

Given: DE || BC; ∠B = 30° ; ∠C = 40°

Formula Used/Theory:-

→ Angle sum property

Sum of all angles of triangle is 180°

→ if 2 lines are parallel then their corresponding angles will be equal

As DE || BC

And AB is transverse

x = 30° ∵ Corresponding angles

As DE || BC

And AC is transverse

y = 40° ∵ Corresponding angles

By angle sum property in Δ ADE

x + y + z = 180°

30° + 40° + z = 180°

z = 180° -70°

z = 110°

Result:- The value of x;y;z is 30°;40°;110° respectively