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