In the given figure if l ∥m, then find x, y and z.

1.	In the given figure if l ∥m, then find x, y and z.
Answer» Given l ∥m and AC is transversal. z = 40° (Alternate interior angles) l ∥m and AB is transversal and x + (y + z) = 180° (co-interior angles are supplementary) x + y + z = 180° (x + y) + 40° = 180° (co-interior angles are supplementary) (∵ z = 40°) x + y + 40° = 180° x + y + 40°-40° = 180° – 40° ∴ x + y = 140° But x = y (given) 2x = 140° ∴ x = 140°/2 = 70° = y So, x = 70°, y = 70° and z = 40° l\|\|m and ac is the transversal so z=40 degree ( alternate interior angle) x=60 degree ( alternate interior angle) y= 180-(60+40)=80 degrees

Answer»

Given l ∥m and AC is transversal.

z = 40° (Alternate interior angles)

l ∥m and AB is transversal and x + (y + z) = 180° (co-interior angles are supplementary)

x + y + z = 180°

(x + y) + 40° = 180° (co-interior angles are supplementary) (∵ z = 40°)

x + y + 40° = 180°

x + y + 40°-40° = 180° – 40°

∴ x + y = 140°

But x = y (given)

2x = 140°

∴ x = 140°/2 = 70° = y

So, x = 70°, y = 70° and z = 40°

l||m and ac is the transversal

so z=40 degree ( alternate interior angle)

x=60 degree ( alternate interior angle)

y= 180-(60+40)=80 degrees

Discussion