In the adjoining figure, measures of some angles are given. Using the

1.	In the adjoining figure, measures of some angles are given. Using the measures, find the values of x, y, z.
Answer» i. ∠NET = 100° and ∠EMR = 140° ∠EMN + ∠EMR = 180° ∴ z +140° =180° ∴ z = 180° -140° ∴ z = 40° ii. Also, ∠NET + ∠NEM = 180° [Angles in a linear pair] ∴ 100° + y = 180° ∴ y = 180° – 100° ∴ y = 80° iii. In ∆ENM, ∴ ∠ENM + ∠NEM + ∠EMN = 180° [Sum of the measures of the angles of a triangle is 180°] ∴ x +80°+ 40°= 180° ∴ x = 180° – 80° – 40° ∴ x = 60° ∴ x = 60°, = 80°, z = 40°

In the adjoining figure, measures of some angles are given. Using the measures, find the values of x, y, z.

Answer»

i. ∠NET = 100° and ∠EMR = 140°

∠EMN + ∠EMR = 180°

∴ z +140° =180°

∴ z = 180° -140°

∴ z = 40°

ii. Also, ∠NET + ∠NEM = 180° [Angles in a linear pair]

∴ 100° + y = 180°

∴ y = 180° – 100°

∴ y = 80°

iii. In ∆ENM,

∴ ∠ENM + ∠NEM + ∠EMN = 180° [Sum of the measures of the angles of a triangle is 180°]

∴ x +80°+ 40°= 180°

∴ x = 180° – 80° – 40°

∴ x = 60°

∴ x = 60°, = 80°, z = 40°