Question

In triangle XYZ exterior ∠ = 110°, ∠ = 2° and ∠ = 3°. Find x.

Answer 1

Answer:

In ∆XYZ we have,

→ ∠X = 70°

→ ∠Z = 40°

So,

→ ∠X + ∠Y + ∠Z = 180° { By angle sum property. }

then,

→ 70° + ∠Y + 40° = 180°

→ ∠Y + 110° = 180°

→ ∠Y = 180° - 110°

→ ∠Y = 70°

now,

→ ∠XYZ + ∠XYW = 180° { Linear pair. }

→ 70° + ∠XYW = 180°

→ ∠XYW = 180° - 70°

→ ∠XYW = 110° (Ans.)

Method (2) :-

→ ∠XYW = ∠YXZ + ∠YZX { Exterior angle is equal to sum of opposite interior angles. }

→ ∠XYW = 70° + 40°

→ ∠XYW = 110° (Ans.)

Step-by-step explanation: