Question

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

Answer 1

DE || BC and AB is a transversal.

∴ ∠ADE = ∠DBC  ...[Corresponding angles]

⇒ x = 30°

Now, DE || BC and AC is a transversal.

∴ ∠AED = ∠ECB  ...[Corresponding angles]

⇒ y = 40°

In ∆ABC,

∠A + ∠B + ∠C = 180°  ...[Angle sum property]

⇒ z + 30° + 40° = 180°

⇒ z = 180° – 40° – 30° = 110°

Thus, x = 30°, y = 40° and z = 110°.