Find the measure of angle z in each of the following figures.

1.	Find the measure of angle z in each of the following figures.
Answer» (i) m and n are parallel lines l is the transversal Then interior angles that lie on the same side of the transversal are supplementary ∴ z + 31° = 180° z + 31° – 31° = 180° – 31° z = 149° (ii) m and n are parallel lines, l is the transversal Interior angles that lie on the same side of the transversal are supplementary ∴ z + 135° = 180° z + 135° – 135° = 180° – 135° z = 45° (iii) m and n are parallel lines l is the transversal exterior angles that lie on the same side of the transversal are supplementary. ∴ z + 79° = 80° z + 79° – 79° = 180° – 79° z = 101° (iv) m and n are parallel lines and l is the transversal. Corresponding angles are equal z + 22° = 180° z + 22° – 22° = 180° – 22° z = 158°

Answer»

(i) m and n are parallel lines l is the transversal

Then interior angles that lie on the same side of the transversal are supplementary

∴ z + 31° = 180°

z + 31° – 31° = 180° – 31°

z = 149°

(ii) m and n are parallel lines, l is the transversal

Interior angles that lie on the same side of the transversal are supplementary

∴ z + 135° = 180°

z + 135° – 135° = 180° – 135°

z = 45°

(iii) m and n are parallel lines l is the transversal exterior angles that lie on the same side of the transversal are supplementary.

∴ z + 79° = 80°

z + 79° – 79° = 180° – 79°

z = 101°

(iv) m and n are parallel lines and l is the transversal. Corresponding angles are equal

z + 22° = 180°

z + 22° – 22° = 180° – 22°

z = 158°

Discussion